Methods for post-harvest crop quality management

ABSTRACT

Embodiments of systems and approaches for managing post-harvest crop quality and pests are described. Such a system may include a plurality of edge devices each comprising sensor components and collectively forming a mesh network, for measuring the local physical environment within stored crops and, for example, transmitting the measurements to a service from within the crop storage area. In certain embodiments, such a system may be used to manage post-harvest crops and storage areas—for example, approaches are described for determining fumigation treatment duration, determining phosphine dosage, determining heat treatment duration, and determining safe storage time for crops.

CROSS REFERENCE TO RELATED APPLICATIONS

This nonprovisional application claims the priority benefit of U.S.Provisional Patent Application No. 62/500,294, filed on May 2, 2017, thedisclosure of which is incorporated herein by reference in its entirety.

TECHNICAL FIELD

The disclosed embodiments relate generally to post-harvest cropmanagement, and more particularly, to methods and systems for managingcrop quality and pests, e.g., using agricultural sensors, dataanalytics, crop storage and pest management techniques.

BACKGROUND

For centuries the global food and agriculture industry has toleratedsignificant post-harvest waste, presently estimated at approximately $1trillion annually. World population is expected to reach 10.5 billion by2050, further exacerbating global food availability and securityconcerns. According to research data, food supplies would need toincrease by 60% (estimated at 2005 food production levels) in order tomeet the food demand by 2050. Food availability and accessibility canvastly improve by increasing production, enhancing logistics, andreducing waste. Thus, reduction of post-harvest waste is a criticalcomponent of ensuring future global food security.

Additionally, health and safety concerns feature high on the agendas ofgovernments and regulators. In this respect, the application ofagrichemicals needs to be monitored with advanced technology, to ensureproper use (adherence to precise pest control protocols), environmentalsafety (managing stored product pests and controlling tolerance andresistance to pesticides) and operator safety (controlling leaks ofharmful toxic substances).

End users in this field, such as farmers, operators of storage andlogistics facilities, agronomists, food scientists, pest controltechnicians and quality control experts, have used certain methods inthe prior art to combat post-harvest waste and its root causes includingpest infestations. These methods have employed technology conceivedseveral decades ago, to perform functions such as fumigation chemical(i.e. fumigant) dosage monitoring, insect infestation detection,spoilage detection. Our assessment revealed that none of these legacysolutions and methods in the prior art effectively addressed thetrillion-dollar waste problems. Moreover, prior art methods forpost-harvest monitoring and quality control have also been manual,error-prone, cumbersome, not scalable, outdated and impractical. Theyhave also been costly without resultant benefits. Specifically:

-   -   Draeger-type fumigant meters have the form of tubes. These        require a lot of manual effort by experienced operators. There        are hazards related to their use. Data is typically recorded by        pen and paper.    -   Certain electronic equipment vendors are offering measurement        devices for fumigation monitoring. These require special        plumbing for sampling fumigant levels inside storage areas, are        difficult to operate and are usually practical only for        infrequent sampling. The data collected is not practically        correlated with proper fumigation protocols or insect mortality        statistics.    -   Certain crop silo monitoring solutions focus specifically on        temperature tracking to detect spoilage as it occurs. They        employ old technology (wired thermocouples) and are difficult to        install. They also malfunction or get completely destroyed in        the presence of fumigant gas. Consequently, when a spoilage        hotspot is detected, it is usually already too late to take        corrective action.    -   Insect collectors and detectors such as pheromone traps require        manual inspection. Electronic products for insect detection that        can transmit insect population data cannot be placed inside bulk        product where insects may take refuge. The data collected is not        correlated with pest management parameters (such as recent        fumigation dosages and durations) or environmental conditions        (such as temperature, humidity).    -   Certain methods in the prior art provide computational means for        assessing properties related to the spoilage of crops (such as        grains) in storage, by estimating key parameters such as product        moisture based on parameters that can be readily observed (such        as product temperature and ambient relative humidity). However,        these tools are of limited accuracy and usefulness as storage        microclimate may change unpredictably (e.g. during a hot and        humid weather spell) and thus render any initial estimates        invalid. Moreover, the initial conditions of a stored product        may not be fully known—e.g. unknowingly mixing a quantity of        damp and infested grain with a larger quantity of drier and good        quality grain may spread the spoilage and infestation to the        entire lot of grain.    -   Researchers in this field have resorted to numerical analysis        techniques such as Computational Fluid Dynamics (CFD)        simulations to predict the effects of climate conditions on        stored commodities. However, these visionary approaches have not        materialized into convenient and handy tools for the actual end        user (who is typically not expert in numerical analysis) as they        have been overly complicated, not easy to control and re-use and        not generic enough to address a good variety of commodity        storage scenarios. Besides, these techniques have fallen short        of correlating concurrently updated physical parameters with        biological effects related to grain spoilage and quality        degradation.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts an exemplary post-harvest crop management system inaccordance with some embodiments of the invention;

FIG. 2A and FIG. 2B depict exemplary edge devices in accordance withsome embodiments of the invention;

FIG. 3 depicts an exploded view for an exemplary edge device inaccordance with some embodiments of the invention;

FIG. 4 shows exemplary components of an edge device in accordance withsome embodiments of the invention;

FIG. 5 depicts an exemplary sensor circuit diagram in accordance withsome embodiments of the invention;

FIG. 6 depicts an antenna elevation radiation pattern for an exemplaryedge device in accordance with some embodiments of the invention;

FIG. 7 depicts an antenna azimuthal radiation pattern for an exemplaryedge device in accordance with some embodiments of the invention;

FIG. 8 depicts an exemplary calibration apparatus for an edge device inaccordance with some embodiments of the invention;

FIG. 9A and FIG. 9B show an exemplary post-harvest crop management userinterface in accordance with some embodiments of the invention;

FIG. 10A and FIG. 10B show an exemplary post-harvest crop managementuser interface in accordance with some embodiments of the invention;

FIG. 11A and FIG. 11B show an exemplary post-harvest crop managementuser interface in accordance with some embodiments of the invention;

FIG. 12 shows a flow chart for an exemplary process concerningdetermining the duration of a fumigation in accordance with someembodiments of the invention;

FIG. 13 shows a flow chart for an exemplary process concerningdetermining a fumigant dosage in accordance with some embodiments of theinvention;

FIG. 14 shows a flow chart for an exemplary process concerningdetermining the duration of a heat treatment in accordance with someembodiments of the invention;

FIG. 15 shows a flow chart for an exemplary process concerningdetermining the safe storage time for a post-harvest crop in accordancewith some embodiments of the invention;

FIG. 16 shows exemplary clusters of temperature traces from heattreatments in accordance with some embodiments of the invention;

FIG. 17 shows exemplary temperature traces from heat treatments inaccordance with some embodiments of the invention;

FIG. 18 shows an exemplary fumigation treatment course exhibitingfumigant leakage in accordance with some embodiments of the invention;

FIG. 19 depicts a block diagram of an exemplary computing system inaccordance with some embodiments of the invention;

FIG. 20 shows a flow chart for an exemplary process concerning theimproved predictions for grain condition and safe storage time.

DETAILED DESCRIPTION

Embodiments of apparatuses, computer systems, computer readable mediums,and methods for post-harvest crop quality and pest management aredescribed. For example, embodiments described herein provide a solutionthat effectively combats spoilage root causes, such as mycotoxins andinsects, and guides end users to efficient pest management inpost-harvest storage of agricultural commodities. The solution may bebased on cloud-connected wireless sensors, real-time data monitoring,data analytics and computational fluid dynamics simulations.

Embodiments described herein effectively resolve the shortcomings ofprevious strategies, to provide efficient post-harvest crop and foodproduct protection and quality management. It efficiently addresses the$1 trillion waste root causes and brings benefits that can positivelyand dramatically impact food safety and agriproduct abundance in thefuture. The inventions achieve these goals by providing fully automated,real-time, in situ (i.e. inside product storage areas) monitoring offumigants and storage conditions, by coupling sensors with dataanalytics and cognitive methods, and by thus driving predictions andprescriptions of fumigant distribution, pest treatment parameters,insect mortality and repopulation, spoilage risks, stored crops qualitymetrics and several other related parameters and end user guidelines.

As described below, edge devices containing sensors may be used todirectly measure physical descriptors in situ. The edge devicespreferably support self-organizing, ad-hoc mesh networking (e.g., toavoid the need for fixed infrastructure) and may be designed in such away to comply with the needs in the various industrial and, often, harshenvironments in which they function, both in terms of mechanical andelectronic robustness but also in terms of wireless communication.

Computational fluid dynamics approaches described below permitpredicting granular fumigation treatment durations and recommendeddosages for new crop storage areas, even when no historical data isavailable. The analytical approaches described below include monitoringand guiding heat treatments by detecting anomalies and alarm conditions,replacing and coping with incorrect sensor readings, with the benefit ofbeing computationally efficient and accordingly taking less time toobtain results.

Further, this system can achieve further unsupervised learning bycorrelating real-time insect population data to fumigant levels.Additionally, we can combine CFD simulation with sensor data andautomatically (i.e. via machine learning methods) adjust the correctionfactors in CFD to match actual data streams, and subsequently use the‘trained’ CFD simulation to make accurate long-term predictions. Thisapplies to both predictive pest management and crop spoilage detectionuse cases.

FIG. 1 depicts an exemplary post-harvest crop quality and pestmanagement system 100. Components of system 100 may be positionedrelative to a crop storage area 106 for storing a harvested crop, suchas rice or wheat. A collection of edge devices 102 may be placed withinthe crop storage area 106, such that they may be used to measurephysical features (e.g., temperature or gas concentration) of theenvironment local to each respective edge device 102 in differentlocations within the crop storage area. For example, edge devices may bemounted to the walls of the storage area, suspended on wires such thatthe edge devices are buried within bulk crop (e.g., surrounded bygrains), and/or positioned between containers of crops or agriculturalmaterials such as sacks of flour. Wires or other attachments may be usedin order to easily retrieve the edge devices as needed, e.g., uponcompletion of a fumigation.

In system 100, the edge devices 102 are configured to form a wireless adhoc network, such as a mesh network, to wirelessly transmit dataincluding the measurements concerning the local environment to a network110 via a gateway device 104 for connecting the network of edge devicesto network 110. Each edge device 102 may be associated with a uniqueidentifier that can be associated with the measurements made by therespective device, in order to correlate the measurements with alocation within the crop storage area. When the edge devices areconfigured as a mesh network, data transmission from within the cropstorage area is robust, as multiple wireless connections between theedge devices provide redundancy in such a topology. For example, one ormore edge devices (e.g., 102 a) may act as a relay, providing anindirect communication link between other edge devices (e.g., 102 b) andthe gateway device 104. Because of their shared design configurations,any individual edge device 102 may function as a relay. In certainembodiments, system 100 includes local data store 108, communicativelycoupled to the gateway 104, for maintaining an on-site back-up for themeasurement data from the edge devices. Additional discussion regardingwireless transmission is provided below, for example in connection withFIG. 6.

Network 110 may be a conventional computer network and/or network ofnetworks (e.g., a local area network, wide area network, and/or theInternet). In certain embodiments, one or more computing devices 114communicatively coupled to the gateway 104 over network 110 hosts aserver 116, such as an HTTP server, and an application 120 thatimplements aspects of the post-harvest crop quality and pest managementsystem in accordance with embodiments of the present invention.Application 120 may perform analytics on measurement data received fromgateway 104, and stores same, preferably along with copies of themeasurement data, in a remote data store 122. Remote data store 122 maybe a dedicated storage appliance, or may be cloud-based storageaccessible to computing device 114.

Application 120 may support an Application Programming Interface (API)118 providing external access to methods for initiating analyses andaccessing remote data store 122 via server 116. In certain embodiments,client applications such as web browsers running on user device(s) 112may access application 120 via its API 118 and through server 116 usingprotocols such as HTTP or FTP (see, e.g., FIGS. 9-11 showing exemplaryuser interfaces for a user device 112 discussed in detail below). Incertain embodiments, user device 112 may be a laptop or desktopcomputer, a mobile device such as a smart phone, or a wearable devicesuch as a smart watch.

Edge Device

FIG. 2A depicts embodiments 201 and 209 of edge device 102, and FIG. 2Bdepicts an embodiment 213 of edge device 102. As used herein, edgedevices 102 are devices that are configured to take measurements ofphysical attributes of the environment local to the respective edgedevice, and are configured as a group to form a wireless ad hoc network,such as a mesh network, to wirelessly transmit data including themeasurements. In certain embodiments, edge devices are more specificallyconfigured to have certain additional features as described throughoutthis specification. Embodiment 201 has a generally cylindrical housing.In certain embodiments, the housing includes vents 206 which areopenings allowing air surrounding the edge device to diffuse into andout of a chamber within the cap 200, permitting detection of, e.g.,moisture content and/or gases within the environment local to the edgedevice (e.g., at a location within crop storage area 106). In certainembodiments, the vents 206 are two or more holes or pores arranged in agrid. In certain embodiments, the vent holes are one or more circular oroval-shaped holes. In certain embodiments, the vents are microholes—i.e., with a diameter in the tens of micrometers. In certainembodiments, the vents may be shaped like a curved slit (e.g., as shownin embodiment 213 in FIG. 2B) or straight slit, where the slit has alength of about half a millimeter. In certain embodiments, a particularvent configuration (e.g., regarding hole number, size, shape, and/orlayout) may be used for a corresponding type of measurement such that ahousing with a first vent arrangement is used for, e.g., phosphineconcentration sensing, and a second housing with a second ventarrangement is used for, e.g., humidity sensing. For example, particularvent configurations can improve sensor accuracy and a faster return tozero gas by facilitating the flow of the target gas over a sensor'sactive surface. In certain embodiments, a single vent configuration maybe optimized for two or more sensing tasks (e.g., phosphine and humiditysensing).

The housing 203 may be assembled from components such as the cap 200that mates with an upper housing 202, the upper housing connecting to alower housing 204. In certain embodiments, the cap, upper housing, andlower housing are threadibly coupled to one another, for example via afirst threaded portion of the cap 200 mating with a second threadedportion of the upper housing 202, and a third threaded portion of theupper housing 202 mating with a fourth threaded portion 212 of the lowerhousing 204. In other embodiments, bayonet couplings, compressioncouplings, pin-and-groove couplings, or combinations thereof may be usedinstead of, in addition to, or in combination with threaded couplings.Static couplings are preferred, in order to provide rigidity to theoverall housing, but in some circumstances flexible couplings may beemployed for situations where edge devices need to conform to specificrecesses or other areas in a crop storage area. In certain embodiments,connections between components of the housing may be permanently sealed,or may reversibly join together.

In certain embodiments, the edge device 102 may include a magnetic ring208 and a switch suppress ring 210. Magnetic ring 208 is acircumferential ring that includes a magnet. The magnetic ring 208 ismounted on a bearing or other surface and allowed to swivel, at leastpartially, azimuthally around the housing 203. In this way, theassociated magnet is translated circumferentially and, as discussedbelow, will cause a Reed switch inside the housing to open or close,depending on the direction of movement. The opening and closing of theReed switch will turn the edge device off and on, respectively. In otherembodiments, the magnetic ring may be fashioned to be translatedvertically, parallel to the longitudinal axis of the edge device, andthereby control the opening and closing of the Reed switch. However, insuch embodiments, detents should be provided, or a sufficient frictionfit maintained, so that the magnetic ring does not translate between itsopen and closed positions unintentionally. In still further embodiments,a magnetic ring may be omitted in favor of a capacitive or resistiveswitch that is used to control the operational state of the edge device(e.g., according to a user's touch operation).

The housing 203 components (e.g., cap 200, upper and lower housing 202and 204 of embodiment 201) and portions of the magnetic ring and switchsuppress ring may be formed from a material such as plastic (e.g., anacetal plastic such as an acetal copolymer or acetal homopolymer). Incertain embodiments, the material used for the housing should becorrosion-resistant in order to protect the internal electronics andother components from toxic gases used in agricultural fumigation.Desirable properties of the housing material include, for example,resistance to high- and low-pH solutions (e.g., fuels and solvents), lowporosity, high stability, and minimal sensitivity to high and lowtemperatures.

FIG. 2B shows an exemplary embodiment 213 of an edge device 102, inwhich the housing is largely bell-shaped and includes a handle 218. Theedge device may include an indicator band 216 and an indicator light214. Indicator bands and lights may turn on or off or change color toindicate the operational status of the edge device—for example, theindicator may flash or turn on to indicate states such as: the edgedevice is on, is collecting data, is transmitting data, is ready to pairwith a network, is performing a firmware update, or is in an errorstate.

FIG. 3 depicts an exploded view for an embodiment 300 of edge device102. In embodiment 300, the cap 200 includes vents 206 arranged in twooffset stacked rows, each row having approximately 15 beveled orcountersunk openings. In certain embodiments, the vents are arrangedinto one, two, or three rows, and the openings are not beveled and boredperpendicularly to the surface of the cap. In embodiment 300, the cap200 includes a first threaded portion (hidden in FIG. 3) that iscomplementary to the second threaded portion 303 of upper housing 202,such that cap 200 screws onto upper housing 202. The upper housing 202includes a third threaded portion (hidden in FIG. 3), complementary to afourth threaded portion 212 of lower housing 204. A magnetic ring 208and switch suppress ring 210 encircle a portion of the fourth threadedportion 212, and when assembled, are located between the upper housing202 and the un-threaded portion of the lower housing 204.

In embodiment 300, the upper housing 202 contains a sensor opening 305in its upper face, through which an electrochemical gas sensor isexposed to air from the environment (e.g., air that has diffused in viavents 206 in cap 200). The electrochemical gas sensor comprises a sensorcell 306 and a sensor circuit board 308. In one embodiment, the sensorcircuit board is designed around the Texas Instruments LMP91000configurable AFE potentiostat for low-power chemical sensing. FIG. 5 istaken from the data sheet for this component and depicts a functionallayout of the subject potentiostat coupled to an electrochemical gassensor cell as may be used in an edge device 102 of a post-harvest cropmanagement system 100. In this configuration, terminals SCL (clock), SDA(data), and MENB (module enable) define an I2C interface forinterconnection with an appropriate microcontroller. In certainembodiments, a sensor circuit board 308 may use such a potentiostat toprovide data from an electrochemical gas sensor cell to the main circuitboard 324. In certain embodiments, the gas sensor may detect phosphine(PH₃), carbon dioxide (CO₂), ethylene, ammonia (NH₃), or ozone (O₃) byincluding the appropriate sensor cell and sensor circuit board.Phosphine detection may be useful for monitoring fumigation treatments,and carbon dioxide detection may be useful for detecting spoilage, inwhich increased concentrations of carbon dioxide may be indicative ofthe amount of spoilage. In certain embodiments, the same edge device 102can be converted to sense a different gas by swapping the sensor cell306 for an appropriate alternative sensor cell.

Embodiment 300 further includes a main board 324 on which variouscomponents are mounted. As shown in the illustrated example, one or moredaughter boards, such as an antenna board 320 having an antenna 319 forwirelessly receiving and transmitting data from and to other edge nodes102 and/or gateways 104, may also be electrically coupled to the maincircuit board. In general, the main circuit board includes a Reed switch322, a radio frequency (RF) transceiver 326 for modulating data to betransmitted via the antenna 319 and demodulating signals received viathe antenna 319, and a buzzer 332 for generating alert noises andproviding other audio feedback. As noted above, Reed switch 322 is anelectrical switch that is actuated by bringing a magnet 336 (e.g.,nickel-plated neodymium magnet) associated with (e.g., mounted on) themagnetic ring 208 in close proximity. Using a Reed switch allowsactivation/deactivation of the edge device without having to decouplethe upper and lower housings from one another or the expense associatedwith air tight gaskets that would be needed if a toggle or other switcharrangement with components passing though the housing(s) were employed.

The components of the edge device are powered by a battery 330, and themain circuit board includes an appropriate connector 334 for interfacingwith a battery power supply 330. In certain embodiments, the batterypower supply 330 includes one or more lithium thionyl chloride batterycells, which provide the advantage of withstanding high heat, allowingthe edge device to survive high storage temperatures or heat treatments.The main circuit board also includes a controller (e.g., amicroprocessor or similar unit), which, in some embodiments isconfigured (e.g., via firmware stored in a non-volatile memory device)to cause the edge device to enter a low-power sleep state as appropriatefor maximum operational life. One example of such a controller is alow-power microcontroller (MCU) processor, which supports theprogramming of applications and libraries which implementinterconnection with peripheral devices, such as the sensors (e.g., anelectrochemical gas sensor). Such peripherals, based on theirspecifications, may communicate with the MCU either through an analogport or through digital port using communication protocols, such as I2C,SPI, UART, serial, and the like.

The main circuit board also may provide appropriate wiring traces tointerconnect the RF transceiver with the MCU, as well as variousfunction indication lamps or LEDs, and other components of the edgedevice.

When assembled as shown in FIG. 3, the internal components of the edgedevice are maintained in separate internal compartments defined by sealsprovided by o-rings (e.g., upper rubber o-rings 302, small rubbero-rings 312). In this way, corrosive gasses from the environment beingmonitored will not come into contact with sensitive electricalcomponents or the battery cells. The portions of the outer housing arescrewed (or otherwise mounted) together, sealing the internal componentswithin the inner, tubular space, and the housing pieces are securedthrough the use of a countersunk pin 304, which prevents the housingportions from coming loose. The internal components are maintained inthe illustrated geometry using screws 318, various board-to-boardinterconnections 316, interface connectors 310, and screw stand-offs314. In certain embodiments, components exposed to the externalenvironment such as pin 304 and screws 318 may be formed from inoxsteel.

In certain embodiments, the edge device 102 is unique in enabling theuse of electrochemical gas sensors (along with supporting electronicsand wireless transmission) for in-situ placement in commodities and inthe presence of corrosive fumigant gas, such as phosphine. Accordingly,a corrosive-chemical resistant housing with activation via a magneticswitch provide key functionality for such embodiments of the invention.Given that phosphine is a highly corrosive toxic gas, the housing of theedge devices has been designed according to the invention to protect allthe vulnerable electronics from the penetration of gases. Accordingly,in certain embodiments, chemical-resistant o-rings of several diametershave been used in all the openings to seal the housing safely when it isclosed. For example, two o-rings, 30 mm in diameter may be used tosecure the sensor cell opening in the upper housing 202, and a third one(24 mm) may placed atop the sensor cell for extra sealing strength. Incertain embodiments, 60 mm o-rings are used for the sealing of the mainopening of the housing, through which the technicians can access theelectronics and the battery pack. Moreover, the housing can provide asafety layer between the main board and the battery power source toprotect the batteries from being in direct contact with the electronicsboard and/or being pierced, overheated or unstable. Embodiment 300includes two upper rubber o-rings 302 placed between the cap 200 andupper housing 202 to create a seal between an environment-exposedcompartment in the cap 200 and a sealed compartment within the upper andlower housing, four small rubber o-rings 312 to seal the screw holes forscrews 318, and a lower rubber o-ring 338 to seal the interface betweenthe upper and lower housing.

s. 4 shows exemplary components of an edge device 102. Device 102 mayinclude one or more processors 404 (such as the MCU discussed above)that may be in communication with a storage component/memory 402, acommunication module 406 (such as the RF transceiver 326), and a powersystem 414 (e.g., a battery power supply), via bus 412.

Device 102 may include various categories of peripheral sensors (e.g.,416, 418, 420, and 422). For example, edge device 102 may include one ormore gas sensors 416, such as a sensor for detecting the concentrationof PH₃, CO₂, or O₂ in air. Device 102 may include one or more ambientconditions sensor 418, such as a temperature sensor, solar radiationsensor, humidity sensor, wind sensor (speed, direction), and/oratmospheric pressure sensor. (In certain embodiments, ambient conditionsensors 418 that provide measurements to system 100 are housed in anambient condition device 103 that is not an edge device 102, e.g., forpositioning and measuring environmental conditions outside of cropstorage area 106, and that may not participate in the mesh networkcreated by a collection of edge devices 102). Device 102 may include oneor more product conditions sensor 420, such as a temperature or moisturecontent sensor. Device 102 may include one or more heat treatment sensor422, such as a temperature sensor or thermal camera.

Device 102 may include an audio processor 408 and a speaker 410 forplaying sound (e.g., for alerts, as an alternative to a buzzer 332).Communication module 406 may include a subscriber identify module (SIM)card, cellular radio, Bluetooth radio, ZigBee radio, Near FieldCommunication (NFC) radio, wireless local area network (WLAN) radio, GPSreceiver, and antennas used by each for communicating data over variousnetworks. Memory 402 may include one or more types of computer readablemedium, such as RAM or flash memory, and may store an operating system,applications, communication procedures, and data generated by peripheraldevices/sensors.

Edge Device Self-Test

A sensor testing procedure may be used to verify the connection and thefunctionality of the sensor in an edge device. One exemplaryself-testing procedure using a sensor circuit board based on the TILMP91000 shown in FIG. 5 comprises the following steps:

(1) I2C Interface connection check. I2C is a two-wire (SDA, SDCLK)interface, used to transfer serial data. In order to check theconnection of these two wires between the main circuit board and thesensor circuit board, data is written to and read from an LMP91000 lockregister. If the I2C interface connection is functional, the value thatwas written to the register will be properly read therefrom. Otherwise,an error is returned.

(2) Sensor Standard output check: In this step, the output of the sensoris checked in normal conditions (no presence of gas). At first, rawsamples are taken for 150 seconds (1 sample per second), allowing the(new) sensor to settle. Then 20 samples are taken. The average of thesesamples is compared with predefined thresholds. These thresholds wereset after testing 10 brand new sensors and 3 faulty sensors. Usually, afaulty sensor outputs a signal slightly higher than normal (0.52Vinstead of 0.48V). In such instances, an error message (e.g., “FaultySensor”) is returned to the user. If the output is in rage of 1.5 V andabove, there is also the possibility that the output female pin of thesensor circuit board is not properly connected to the male connector pincircuit board. In such instances, an error message (e.g., “Faulty sensoror bad connection to Vout”) is returned. If the result exceeds thethresholds, an error message is returned. The gas sensor is connected tothe analog front end (AFE) of the LMP91000. For communication with theAFE, the I2C interface is used.

(3) Pulse insertion: In the third and last step, a pulse signal isinserted in the Counter Electrode (CE) of the sensor. This isaccomplished by inserting a bias voltage (1% of Vref). With this test, averification that the sensor is successfully attached to the sensorboard is made. For example: R_(TIA) is changed to 7.5 k from the defaultof 35 k; bias polarity is changed to positive from the default ofnegative; bias is changed to 1% from its default of 0%; the biaspolarity is restored back to negative; the bias is restored to 0%; andRTIA is restored to 35 k.

Antenna Design

The antenna must efficiently couple radio frequency energy between theoutside environment and the internal package circuitry. In certainembodiments, the antenna 319 of the edge device is an electrically shortinverted ‘L’ monopole with an orthogonal meander line top plate having atotal line length of approximately a quarter wavelength. The monopoleantenna functions against the solid printed circuit board ground planecounterpoise. The vertical radiation pattern is approximately uniform,similar to that for a full quarter wave vertical antenna, but has anon-uniform horizontal component that is useful for communicationsreliability in complex propagation environments, such as transmittingfrom inside bulk products (e.g., stored grain in a silo). The structureof such an antenna facilitates a considerable reduction in overallpackage height to that needed with a full size vertical radiator.

FIG. 6 shows elevation radiation patterns for antennas of edge device102, and FIG. 7 shows azimuthal radiation patterns for antennas of edgedevice 102. Each figure shows radiation patterns for both horizontal andvertical polarizations. As shown in FIG. 7, the radiation pattern isomnidirectional in the azimuthal plane, which is desirable for thetarget environments, as any horizontally dispersed arrangement of edgedevices throughout the crop storage area should maintain thecommunication flow within the mesh network. In certain embodiments, theantenna is tuned to frequencies such as sub-GHz unlicensed (ISM) bands,specifically the 865 MHz band for the EU/Africa and the 920 MHz for theAmericas. Preferably, the antenna is tuned (by appropriate strapping ofsegments) to minimize losses such that no matching circuit is needed forconnection with the wireless transceiver.

Network Design for Harsh Environments

In certain embodiments, the wirelessly transported sensor readings haveto reach the gateway device 104 through thick obstacles, such as a highdensity of stored product. In addition, industrial facilities such ascontainer yards, flour mills and logistics buildings usually cover largeareas, which make the adoption of wireless communications veryattractive. Achieving reliable wireless communications in such areas,though, is not a trivial issue. Furthermore, the industrial environmentincludes numerous metal constructions (post-harvest grains, dry nuts,tobacco and various other agriproducts which require pest treatment areoften stored in metallic constructions, such as silos and containers)and sources of electromagnetic interference. Therefore, the edge devices102 must communicate not only through obstacles, but also through metal,which creates an even more challenging situation. For these reasons, aset of assistive devices that will act as network repeaters may berequired. In certain embodiments, edge devices 102 may be used asrepeaters.

Battery-Powered and Always-On Repeaters

Edge devices 102 functioning as repeater devices aim to extend networkcoverage and facilitate message forwarding towards the network sink(e.g., the gateway 104). Depending on their installation, theserepeaters may be battery-powered or “always-on” (i.e., supplied withmain power). Both devices offer data forwarding to/from neighboringnodes or repeaters. In addition, repeaters not only convey data fromtheir children-neighbors to the sink, but, in the case ofbattery-powered repeaters, also provide sleep period and clocksynchronization messages to the children/neighbor nodes. That is, whilealways-on devices need not and do not “sleep” in a periodic manner tosave energy, and therefore are able to serve any child-/neighbor-nodewithin their network range even in the case of inter-device clockdrifts, battery powered repeaters must synchronize their clocks withtheir child-/neighbor-node so that the child-/neighbor-nodes do notattempt transmissions while the repeater is asleep. In some networks, acommunication protocol that makes use of sequential message numbers maybe employed so that a repeater will recognize instances of missedmessages from child-/neighbor-nodes. While it is usually not necessaryto have such missed messages repeated (unless the message cycle time isvery long or the environmental conditions being monitored are changingvery rapidly), knowing that messages have been missed may be used as aprompt for the repeater to issue new synchronization messages to itschild-/neighbor-nodes.

Device Calibration

It is desirable to ensure precision and agreement of readings amongseveral edge devices 102. In certain embodiments, precision can beachieved via calibration against prototype gases of known concentration,for example where the edge devices include a gas sensor. Such acalibration process aims to optimize sensors' precision and evaluatetheir readings against reference gases to compensate for sensor agingafter prolonged use and exposure to high fumigant concentration. Theelectrochemical cells (e.g., sensor cell 306) may operate in theamperometric mode based on several layers of electrodes over anelectrolyte reservoir. Due to the fact that the electrolyte volume isfinite, these sensors present aging over time. For the above-mentionedreasons a calibration setup has been designed. FIG. 8 depicts anexemplary fumigant sensing calibration apparatus 800 for an edge device102. In certain embodiments, apparatus 800 uses chemical-resistant tubesconnecting inox (stainless-steel) valves (e.g., three-way valve 808),connectors, and anti-corrosive Vernier valves 806 to exits 812 and a gashood 810. In certain embodiments, the aim of this setup is to calibratethe sensors against 500 ppm and 1000 ppm PH₃ gases carried by nitrogen,or a proper surrogate gas such as SO₂. The apparatus 800 may include airtank 802, fumigant tank 804 a having a lower known concentration offumigant in nitrogen (e.g., 500 ppm phosphine), fumigant tank 804 bhaving a higher known concentration of fumigant (e.g., 1,000 ppmphosphine).

In in certain embodiments, a calibration procedure using an apparatussuch as 800 can be performed at the end user's location (e.g., at thelocation of the crop storage area 106), with the setup described hereinimplemented as a user-owned apparatus. When the device under calibrationwhich is connected to the gas hood 810 is an edge-device 102 accordingto the invention, the calibration coefficients thus obtained can bestored in the cloud platform system disclosed herein (e.g., in remotedata store 122, accessible via API 118), and/or in local data store 108.Thus it becomes possible to not only safely store the calibrationcoefficients in the cloud and conveniently recall them when the edgedevice 102 accesses the platform, but also to provide pre-emptivemaintenance and data analytics tasks. For instance, the platform systemcan inform an end user when an edge device requires factory maintenance;the platform operator can perform quality control by aggregatingcalibration data for all the edge devices connecting to the platform,and thus improve the level of service it provides to end users;moreover, a cognitive system implemented in the cloud platform canprovide increasingly more accurate correction factors, by being trainedon the aggregate datasets produced when various end users performcalibration tasks on their edge devices.

Approaches for Managing Crop Quality

In certain embodiments, data are collected from an agriproduct or foodstorage facility via edge devices 102. The data are uploaded to a cloudserver (e.g., server 116) or to the end user's own intranet (e.g., localdata store 108 on a private network) or private cloud, wherecharacteristics and plots can be viewed and analyzed from anywhere inreal-time on smart devices equipped with the mobile app, and over theinternet via PC, etc. (e.g., via user device 112). Thus, a large amountof data can efficiently be used in optimization of processes, e.g. todetermine the exact duration of treatments such as fumigations, to issuealarm conditions and to predict time and conditions of successfultreatments. The collected readings can be used to predict events andresolve or prevent potential quality issues, along with effectingproductivity improvements based on historical and simulated data.Applying predictive models in real time means an end user can directlyintervene early on in a long-lasting process, predict outcome and avoidfailures.

Real-Time Data Monitoring

Real-time data arriving from edge devices 102 for stored crop qualitymonitoring may include multiple time series depending on the number ofedge devices and respective sensors used, and may be used to create agraphical representation in chronological order. Data visualization isuseful in order to present streaming data. As the sensor readings may bein time-series form, in certain embodiments, line charts are adequatesince trends over time and alerting conditions on specific moments canbe depicted.

Platform

Certain embodiments of the invention concern a service platform that maybe a cloud-based application which provides all the necessaryarchitecture elements for aggregating and presenting data, executing andpresenting cognitive predictive and prescriptive analysis, interactingwith third-party applications, and generating efficient interfaces forend-user interaction.

Architecture

The platform may be based on a microservice architecture. A microservicearchitecture restricts each service to a small set of responsibilitiesand provides it as a black-box component to be used or integrated withother microservices. This provides the advantages of easier testing,scaling and maintenance because each unit is only responsible foritself, and it only needs to comply with its published API definition orinterface for integration.

In certain embodiments, the different microservices are built andorchestrated using the Docker Container Service (Docker, Inc.) whichmakes the system hardware & operating system-agnostic and easilyportable with only a few configuration files enough to deploy thecomplete solution to a new location.

The platform may include these components: (1) Device Communication anddata acquisition; (2) Main API—Authorization provider for the platformto be accessible; (3) Acquired Data Processing (real time rules,analytics, machine learning, etc.); (4) Web or mobile application aspresentation layer.

Device Management

Sensor data (e.g., from sensors of edge devices 102) may provide rawmaterial for the platform. This data is acquired from local sensornetworks that are connected to the cloud through edge gateways (e.g.,gateway 104). The edge gateway may run a fog-agent which is generallyresponsible for gathering the data from the local sensor network andsending them to cloud. The fog agent may also make sure the device iskept connected to the cloud, handle the device to cloud and vice versacommunication, including device telemetry and device managementcommands. Finally, the fog agent may also provide the ability to changethe configuration parameters for the local sensor network and provideremote access to the device (e.g., gateway 104 or edge devices 102).

Application Interface

In certain embodiments, an application interface (e.g., API 118)provides the entry point for the application (e.g., application 120) forany publicly available functionality. This can be used by a front-endweb application as a data source, and also as an API for any interestedconsumer. It also implements authentication and authorization foraccessing different resources based on roles to create different levelsof access for each user.

Data Processing

Data processing concerns the manipulation of raw data (sensor, weather,etc.) after the collection of them. Data may arrive in real time, or ina batch after edge device was offline, from connected edge devices, orservices generating data (such as weather recording and quality metricsfor each process). Upon data receipt the data may be streamlined todifferent consumers whose operation is independent from each other.

Storage

The most basic functionality is to store the data in persistent storage(e.g., NoSQL database, involving remote data store 122) to be availablefor further processing. The data is aggregated in an optimal manner forthe application, in order to be more efficient in storage size andaccess—retrieval performance. In this way the readings are available forany process that requires historical data.

Recipes

Incoming edge device data may be passed through a recipe rule engine andfor each rule that is validated, a predefined action occurs. Recipescomprise rules. Rules may be sets of user defined conditions, concerningthe values of device telemetry. The advantages of this inventioncompared to the other available rule engines include:

(1) Support stateful conditions. Most systems provide logic that canonly be applied on the actual isolated payload of the device, and havemostly to do with simple value operators (greater than, equal, and thelike). In certain embodiments, the platform provides the ability foreach condition to store a state as well as take into account historicdata, for evaluating its result.

(2) Support for multiple simultaneous conditions. When a required logicis too complicated to be evaluated in a single condition, embodiments ofthe platform may provide the ability to define a set of multipleconditions that must be fulfilled in order for the rule to be consideredvalid.

(3) Support for rule prerequisites. In case a rule is relied upon forvalidation of a separate rule, this can be added as a prerequisite forthe former, so that it will only validate when the prerequisite rulevalidates.

For each rule or recipe, when the conditions are valid a set ofpredefined actions can occur. These include sending an email, in-appnotifications, and the like.

Analytics

The platform includes an analytics system. The ability to process rawmetrics and provide helpful insights to the customer is what it mattersthe most for the end user. Certain mechanisms provide intelligence ondifferent aspects and usage scenarios:

Heat treatment predictive analytics, where valuable info is given basedon historic data of previous heat treatments allowing the end user tomake quick decisions for the treatment.

Optimal PH₃ dosage recommendation, for optimal results in a PH₃fumigation process.

Calculation of PH₃ concentration over time inside asset, for anestimation and overview of the fumigation process to take place in anasset.

Estimated time at completion of successful fumigation, based on theactual recorded state of the running process and its compliance withproper procedures.

Safe storage time of stored product, to give the end user the ability toplan accordingly his/her actions having the estimate of product safedates.

The analytics system may function in a complete asynchronous andnon-blocking manner. A basic workflow may include: (1) Analytics Servicereceives a task to be executed; (2) Different types of workers runspecific job types as assigned to them; (3) After the work is done, themain application is signaled with the result.

Presentation Layer

In certain embodiments, the application is cloud based, cross-browsercompatible and its layout is mobile responsive. Web socket communicationis a key characteristic of the application as it depends on real timenotifications and data feed.

In certain embodiments, in the application, the user has the ability tomonitor the devices he/she owns and to view general information andhistorical data of all the entities. In certain embodiments, the mainstructure consists of five main entities, the Activities, the Processes,the Recipes, the Assets, and the Devices. Each entity has its ownproperties and functionality that help the user to monitor, organize andvisualize the provided measurements, incoming from multiple sources.

Devices

The device section contains the user's acquired hardware. It includestwo subsets, the gateways 104 and the edge devices 102. The gateways aredevices that collect the measurements by sensors of the edge devices.The gateway section may display an overview of real time sensor readingsas well as general information about the location of the devices,communication statistics and hardware configuration. The location of thedevices may be a geographic location (e.g., a city name, a zip code, orGPS coordinates) or an internally named location (e.g., “facility 285”).The sensor section may contain specific sensor information such asnotes, unique id and custom names concerning edge devices.

Assets

The Asset section refers to the users' actual properties, likebuildings, storages, warehouses or any other entity at which the userwill place edge devices (i.e., crop storage area 106). In certainembodiments, the user has the functionality to input and store keycharacteristics of the asset. More specifically, the user can input thetype of the asset (warehouse, storage, etc.) its dimensions, itsgeographic location and the type and quantity of the product (crop)stored in it (if any).

Furthermore, in certain embodiments, the user may draw the main area ofthe asset, with the help of a drawing tool, in order to assign thespecific sensors' locations. The sensor/edge device location within theasset may be defined using three-dimensional spatial coordinatesrelative to an origin point. This section may also provide informationregarding the treatments that currently take (or took) place at it andthe condition of the contained stored product based on calculatedQuality Control Metrics (see description of Quality Plan below).

Recipes

In certain embodiments, the Recipe section contains functionality thatallows the user to define conditions regarding the measurements andnotify the user through various channels (in-app notifications, emails,and the like) when these conditions are fulfilled. Conditions mayconcern the status of an asset or the crops within it, as determinedusing an analysis approach provided by the platform. For example, arecipe may be used to define a notification responsive to changes in theestimated time of completion of a particular type of treatment in aparticular asset. These recipes can be assigned and reused in multipleedge device groups or to a single edge device.

Activities

In certain embodiments, the Activity section has two main subsets, theTreatment Plan and the Quality Plan. The Treatment Plan section guidesthrough the user to define various parameters such as the type of thetreatment (Fumigation, Heat Treatment etc.), the items that the userwants to fumigate and their environmental conditions. These parametersmay be used as for calculation of an approximately estimated time tocompletion for the heat treatment or fumigation. The Quality Plansection may prompt the user to enter the environmental conditions oftheir product stored in an asset and as result it returns to the user,metrics and statistics that help the user monitor the quality of thatproduct over time.

Processes

In certain embodiments, the Process section provides the user theability to monitor sensor measurements or various metrics for a specifictime span. In certain embodiments, each process can monitor one ormultiple gateways, specific sensors, quality control metrics or weathercondition readings. The measurements can be displayed in real time intiles or in graph view. Moreover, the user may be able to place the edgedevices as items in the Asset drawing and monitor their measurements.

FIG. 9A and FIG. 9B show an exemplary embodiment of post-harvest cropmanagement user interface (UI) 900, e.g. for a user device 112. UI 900permits viewing and configuring a Treatment Plan. FIG. 9A shows anavigation panel 902, allowing the user to navigate between UIs for adashboard, activities, processes, recipes, assets, devices, andsettings. Editor panel 902 presents options for editing a treatmentplan. For example, treatment type options 904 permit selecting a type oftreatment (e.g., phosphine fumigation). Asset options 906 permit editingproperties of the asset, such as its type, fill percentage, location,volume/dimensions, and type of stored product (e.g., whole wheat). Pesttype options 908 permit selecting one or more pests that may affect theproduct. Treatment options 910 allow selection and calculation of arecommended treatment dosage. FIG. 9B shows analytics panel 912 withineditor panel 903. Analytics panel 912 may present a determination of theexpected treatment duration and a chart view of the expected course oftreatment. For example, as shown in FIG. 9B, for a phosphine treatmentassociated with the user-selected parameters shown in FIG. 9A, analyticspanel 912 presents the expected range of phosphine concentration withinthe asset in a chart view across a period of days of treatment,including a completion indicator 914 to indicate the time at which thetreatment is expected to be complete. In certain embodiments, thetreatment is expected to be complete at the time when less than 1% ofthe identified pests are expected to have survived the fumigation.

FIG. 10A and FIG. 10B show an exemplary embodiment of post-harvest cropmanagement user interface 900, configured with different user-selectedoptions relative to FIG. 9A and FIG. 9B. Additionally, FIG. 10A showsproduct conditions options 1002 within editor panel 903, by which datasources for temperature and relative humidity can be set, as well asexpected leakage of the asset. For example, selecting the “weather”option may cause the temperature or humidity to be set according to athird-party weather information service such as weather.com ordarksky.net using the provided location of the asset, selecting “sensor”will source the temperature or humidity using sensors of one or moreedge devices 102 within the asset or an ambient condition device 103,and selecting “manual” allows the user to directly input the temperatureor humidity. FIG. 10B shows, in analytics panel 912, a determination ofthe expected duration for a phosphine treatment based in part on thetemperature and humidity defined via product conditions options 1002.

FIG. 11A and FIG. 11B show an exemplary post-harvest crop managementuser interfaces 1100 and 1150, e.g. for a user device 112. UI 1100permits viewing and configuring a Process as part of a Quality Plan. UI1100 includes process navigation tabs 1102 for navigating between anoverview, recipes, information, and settings. UI 1100 additionallyincludes a content panel 1104 containing a readings listing 1106 and aprocess analytics panel 1108. Readings listing 1106 may provide areal-time listing of environmental conditions of the stored product(e.g., weather related measurements such as temperature and relativehumidity). In certain embodiments, the readings listing 1106 may presentinformation about an expected safe storage time with respect to anexpected number of days until the product will evidence visible mold,dry matter loss, and/or germination. Such predictions may be based onthe measured environmental conditions. The patterns, in the entire silostorage, of the above parameters, may also be presented in videos ortime series graphs as shown in UI 1150 of FIG. 11B.

Computational Fluid Dynamics

In phosphine fumigations, it is important to ensure that phosphineconcentration exceeds the predefined ppm levels in the entire storagespace, e.g., to ensure insect mortality of 99.9%. In order to increasethe spatial resolution of sensor data, Computational Fluid Dynamics(CFD) models are used. CFD is a branch of fluid mechanics that usesnumerical analysis and data structures to solve and analyze problemsthat involve fluid flows. Computers configured to perform thecalculations required to simulate the interaction of liquids and gaseswith surfaces defined by boundary conditions. In this invention, a CFDmodel is developed specifically to meet the parameters involved infumigations. Among others, results may include phosphine concentrationprofiles for every location (both empty and filled with grain regions),temperature, and air velocity in time. Alternatively or in addition tophosphine, gasses important for stored product condition such as carbondioxide, ethylene, ammonia, or ozone may be simulated in models likethose described below.

FIG. 12 shows a flow chart for an exemplary process 1200 concerningdetermining the duration of a fumigation. To begin, a server (e.g.,server 116) receives measurement data generated by a plurality of edgedevices 102, where the edge devices may be positioned in variouslocations within a crop storage area 106 (1202). (In certainembodiments, an alternate version of step 1202 and process 1200 may beperformed at a computing device that is geographically local to the cropstorage area 106.) Edge devices 102 may be conveniently positioned, ormay be evenly spaced throughout the crop storage area—for example, theedge devices may be positioned so that they are separated by about 1, 5,10, or 20 meters across the floor or separated within a horizontal (x-y)or vertical (y-z) plane of the crop storage area. In certainembodiments, the received measurement data may be, for example,generated by one or more peripheral sensors such as a gas sensor 416, anambient conditions sensor 418, a product conditions sensor 420, or aheat treatment sensor 422. The measurement data may concern the localphysical environment for the corresponding edge device that generatedthe respective measurement—for example, an individual measurement of themeasurement data may be a measurement of temperature, gas/fumigantconcentration, or moisture content for a particular edge device (and,e.g., associated with the physical location of the edge device withinthe crop storage area via an identifier for the edge device), as well asthe specific type of measurement such as “PH₃” and/or the category ofthe type of measurement such as “fumigant concentration”), and thedate/time at which the measurement was taken by the sensor of the edgedevice. Edge device measurements of, e.g., fumigant concentration,temperature, moisture content, and/or relative humidity correspond tothe medium measured at the location of the respective edge device, andthus characterize the air and/or crop at the location. In certainembodiments, the server may additionally receive data from a source thatis not an edge device 102, such as a third-party service providinggeographic weather information for the city hosting the crop storagearea, or a different type of device having an ambient conditions sensor418.

Locations within the crop storage area may be represented as a meshdefining a plurality of three-dimensional cells, such that the physicallocations in the crop storage area are mapped to corresponding cells ofthe mesh (1204). For example, each coordinate position within the cropstorage area (e.g., a physical location) will have a correspondingposition in the coordinate system of the mesh. In certain embodiments,each cell is the same size and shape. In certain embodiments, certaincategories of cells provide a higher resolution representation of thecorresponding regions in the crop storage area 106 compared to lowerresolution representations (e.g., higher resolution representations of aregion are associated with larger numbers of smaller cells).

A system of governing differential equations may be defined to relate aplurality of physical descriptors of the contents of the crop storagearea and the environment of the crop storage area, wherein thedescriptors include the amount of fumigant in the crop storage area(1206). As used herein, “physical descriptors” are quantitative physicalparameters that describe the materials within and at the boundaries ofthe crop storage area and their properties of interest, such as theconcentration, sorption rate, temperature, and velocity of a fumigantgas at a position at a time. The physical descriptors may determined by,for example, transport equations for modeling incompressible fluid flow,heat, and mass transfer of a gas (e.g., where the gas may be afumigant), taking into account temperature and pressure; porous mediumeffects, where the medium is the stored product (crops); a mediumtortuosity effect on diffusion; the effect of sorption of one or moregases by a medium; gas release rate from a dispenser such as a tablet orsachet; and oxidative degradation of the gas. The environment of thecrop storage area may be represented using boundary conditions—e.g.,mass convective boundary conditions and thermal convective boundaryconditions. Such a model according to the invention has not beenpreviously reported using a three-dimensional mesh and associatedequations adapted for three dimensions, and avoids the need to assumesymmetry in the third dimension, an assumption that is not valid formost storage facilities.

The amount of fumigant may be simulated within each cell of the mesh by,for example, setting the initial values of a subset of the physicaldescriptors using the received measurement data, including thetemperature and relative humidity, and using numerical analysis of thesystem of governing differential equations to approximate the values ofthe physical descriptors at a range of time points, includingapproximating the value of the amount of fumigant (1208). For example,the initial values of physical descriptors may be set using edge device102 measurements of temperature and/or relative humidity. In such anexample, the actual measured value of the physical descriptor may beused for the initial value of the corresponding location/position in themesh, and initial values for intermediate locations may be extrapolatedbased on an average of surrounding edge device position measurements.Numerical approximations of the solution(s) to the system of governingdifferential equations may be obtained using a CFD solver. Accordingly,the system may be simulated to approximate its behavior throughout themesh/crop storage area at later time points, including approximating thefumigant concentration profile for the crop storage area at later timepoints.

The amount of living invertebrate pests (i.e., undesirable insects,arachnids, nematodes, and gastropods), and their pre-adult stages (e.g.eggs, larvae, pupae) may be determined for the range of time pointsbased on the simulated amounts of fumigant (1210). The time pointsassociated with an amount of living pests that is less than or equal toan acceptable amount may be identified (1212). More specifically, theeffect of a fumigant on the mortality of invertebrate pests is based onthe level of fumigant concentration and the duration of exposure. Thefumigant concentration profiles determined in step 1208 may be used todetermine whether, at a particular time point, there may be any livepests remaining in the crop storage area. For example, the simulationmay determine a portion of the mesh may be associated with a relativelylow concentration of fumigant two hours after commencing a fumigationwith a particular dose of fumigant. Even if other portions of the meshwould represent portions of the crop storage area in which the pestshave been exposed to a sufficiently high concentration of fumigant for asufficient period of time, this example would indicate that a higherdose or longer fumigation is necessary to effectively fumigate thestorage area. In certain embodiments, the acceptable amount of livingpests may be zero, an amount of pests that is too low to be measured, orless than 1% of the pests remaining alive.

A continuously or periodically updated estimate for the time remainingfor a complete fumigation may be reported, e.g., to a client device suchas user device 112 (1214). The time remaining may be, for example, theestimated date and time until the acceptable amount of livinginvertebrates will be achieved (i.e., the time when the fumigation willbe complete). In certain embodiments, the positions with worst-case(lowest) fumigant levels are reported. Such information may be useful toidentify an optimal location for placing a fumigant dispenser, or toidentify an optimal location for placing an edge device in order tomonitor the most challenging-to-fumigate locations inside the cropstorage area.

In certain embodiments, the edge devices are used to measure the actualconcentration of a fumigant, and regions of discrepancies between actualand simulated concentrations of fumigant are used to troubleshoot thefumigation. For example, additional fumigant dispensers may be added toareas with low fumigant concentrations, air recirculation systems may beswitched on or off, or the discrepancy may indicate leakage of fumigantfrom the crop storage area.

In fumigation treatments, weather data (e.g., temperature, pressure,relative humidity, solar radiation, and wind measurements) may be usedto evaluate the degassing rate of phosphine, to calculate accuratevalues of the thermodynamic and transport properties of air atatmospheric pressure (air properties) and to properly parameterize thethermal convective boundary conditions. Based on the resulting model,the expected phosphine concentration may be approximated for the cropstorage area. If the edge device sensor readings are below the predictedvalues, this may be a sign of significant leakage. Accordingly,additional fumigant should be placed in the storage. FIG. 18 shows anexemplary fumigation treatment course exhibiting fumigant leakage. InFIG. 18, the predicted average concentration of phosphine is shownoverlaid with the actual measured concentration from a single edgedevice.

* * * * *

EXAMPLE 1 A CFD Model for Estimating Phosphine Concentrations Example1.1 Governing Transport Equations

The CFD solver may be implemented using OpenFoam v.3.0.1 (OpenFOAMFoundation, Ltd.) in order to solve the following transport equationsfor incompressible fluid flow, heat and mass transfer, accounting forporous media effects:

$\begin{matrix}{\mspace{79mu} {{\nabla u} = 0}} & (1) \\{{\frac{\partial u}{\partial t} + {\frac{1}{\varphi}u\; {\nabla u}}} = {{{- \varphi}{\nabla p}} + {v{\nabla^{2}u}} - {\varphi \; \frac{v}{K}u} - {\varphi \; \frac{F_{e}}{\sqrt{K}}{u}u} + {\varphi \; g\; \beta \; \left( {T - T_{ref}} \right)} + {\varphi \; g\; {\beta_{c}\left( {C - C_{ref}} \right)}}}} & (2) \\{\mspace{79mu} {{\frac{\partial T}{\partial t} + {\varphi \; \frac{\left( {\rho \; C_{p}} \right)_{f}}{\left( {\rho \; C_{p}} \right)_{eff}}u{\nabla T}}} = {\frac{k_{eff}}{\left( {\rho \; C_{p}} \right)_{eff}}{\nabla^{2}T}}}} & (3) \\{\mspace{79mu} {{{\varphi \frac{\partial C}{\partial t}} + {\varphi \; u{\nabla C}}} = {{\varphi {\nabla^{2}\left( {\frac{D_{m}}{\tau}C} \right)}} - {\varphi \; B_{1}C} + {B_{2}q}}}} & (4) \\{\mspace{79mu} {\frac{\partial q}{\partial t} = {{{- B_{3}}q} + {\varphi \; B_{4}C}}}} & (5)\end{matrix}$

In the above equations (1)-(5), u is the velocity vector, and p, T, andC are the pressure, temperature, and gas concentration in air,respectively. D_(m) is the binary diffusion coefficient [m² s⁻¹].Buoyancy forces created by both temperature and concentration gradientsare considered in the momentum equations using the Boussinesqapproximation. Under the Boussinesq approximation the variation ofdensity ρ with temperature T is linear, according to ρ=ρ_(ref)−ρ_(ref)62 (T−T_(ref))). The volumetric coefficient of thermal expansion β isgiven by

$\beta = {{{- \frac{1}{\rho}}\left( \frac{\partial\rho}{\partial T} \right)_{p}} = \frac{1}{T}}$

for ideal gases

and the species expansion coefficient β_(c) is given by

$\beta_{c} = {{{- \frac{1}{\rho}}\left( \frac{\partial\rho}{\partial C} \right)_{p}} = {\frac{1}{\rho_{air}}\left( {\frac{M\; W_{air}}{M\; W_{gas}} - 1} \right)}}$

for ideal gases

where MW_(air) and MW_(gas) are the molecular weights of air anddispersed gas (e.g. phosphine), respectively.

Example 1.2 Porous Media

In order to account the effect of grains to the fluid flow, the grainsare assumed to be a porous medium. Flow in porous layers is described bythe Darcy-Brinkman formulation. The geometric function F_(e) and thepermeability K of the porous medium are related to the porosity φ basedon Ergun's experimental investigations:

$\begin{matrix}{F_{e} = \frac{1.75}{\sqrt{150\; \varphi^{3}}}} & (6) \\{K = \frac{\varphi^{3}d_{p}^{2}}{150\left( {1 - \varphi} \right)^{2}}} & (7)\end{matrix}$

The effective properties (ρC_(p))_(eff) and k_(eff) are calculated as afunction of the fluid and porous material:

(ρC _(p))_(eff)=(1−φ)(ρC _(p))_(solid)+φ(ρC _(p))_(f)   (8)

k _(eff)=(1−φ)k _(solid) +φk _(f)   (9)

The above formulation is valid when thermal equilibrium exists betweenthe fluid and the porous medium. Soret effect (mass flux produced by atemperature gradient) and Dufour effect (heat flux produced by aconcentration gradient) are considered negligible.

OpenFOAM offers the flexibility of modeling incompressible flow throughporous medium, using the explicitPorositySource feature of thefvOptions, which adds the Darcy-Forchheimer source terms (Eqs. 6 and 7)in the momentum equation (Eq. 2). In OpenFoam notation theDarcy-Forchheimer equation is described as:

S _(i) =−vdu−1/2f|u|u   (10)

Correlating the above equation with Eqs. 6 and 7, d and f coefficientscould be calculated as:

$\begin{matrix}{{d = {\varphi \; \frac{1}{K}}}{f = {\varphi \; \frac{2\; F_{e}}{\sqrt{k}}}}} & (11)\end{matrix}$

The implementation of porosity term in the momentum equation isnecessary in order to produce results with high levels of accuracy.

Example 1.2.1 Tortuosity

Consider a scenario where the species only diffuse within a constantdensity fluid in a homogeneous porous medium without a source or sink.In this case, the solution of mass transport equation does not depend onporosity since diffusion time and length scales are not functions of theporosity. This implies that the concentrations will be identical whenthe user stipulates 0% or 100% porosity, an incorrect result. Torepresent the role of porosity on ordinary molecular diffusion, thediffusion coefficient in Eq. 4 must be scaled with tortuosity (Shen andChen, 2007)). Tortuosity is defined as the ratio of the length of thecurve to the distance between the ends of it. There are two approachesin the literature involving tortuosity on the effective diffusivitycoefficient:

$\begin{matrix}{D_{eff} = \frac{D_{m}}{\tau}} & (12) \\{D_{eff} = \frac{D_{m}}{\tau^{2}}} & (13)\end{matrix}$

The first (Eq. 12) is proposed by He et al. (2014) and is also the oneused for the present OpenFoam solver. The second approach (Eq. 13) isproposed by (Shen and Chen, 2007). In their study, Neethirajan et al.(2008) calculated τ=2.4 for wheat and Ahmdad et al. (2012) measured τbetween 38 and 275 depending on water-cement ratio, cement content andcoarse-fine aggregate ratio.

Example 1.3 Sorption

Phosphine is adsorbed by grain at differing rates depending on the graintype. Sorption can reduce the concentrations of fumigation doses tosublethal levels before grain has been disinfested. A model to predictfumigant losses due to sorption is considered necessary. Researchers(Darby, 2008) have suggested that the relationship between the fumigantconcentration in the interstices between the grain, C, and the averageconcentration of fumigant within the grain kernel q, is modelled by Eqs4 and 5 which assert that phosphine is absorbed into the grain and atthe same time also degrades in air. The coefficients B₁, B₂, B₃ and B₄,are independent of C and q.

$\begin{matrix}{B_{1} = \frac{S_{sorp}k_{f}}{B_{fill}}} & (14) \\{B_{2} = \frac{S_{sorp}k_{f}}{B_{fill}F}} & (15) \\{B_{3} = {\frac{S_{sorp}k_{f}}{\left( {1 - \varphi} \right)F} + k_{bind}}} & (16) \\{B_{4} = \frac{S_{sorp}k_{f}}{\left( {1 - \varphi} \right)}} & (17) \\{B_{fill} = {\phi + \frac{1 - R_{fill}}{R_{fill}}}} & (18)\end{matrix}$

S_(sorp) is the specific adsorption surface area

k_(f) is a linear mass transfer coefficient

F is the partition relation coefficient

k_(bind) is the coefficient for irreversible reaction/binding of theadsorbed fumigant in the grain kernel

Example 1.4 Insect Mortality

It is known that the effect of phosphine on the mortality of graininsects is due to both the level of the phosphine concentration and thetime of exposure. According to Collins et al. (2005) and Isa et al.(2016) an extinction indicator function e(x, t) could be defined as:

$\begin{matrix}{{e\left( {x,t} \right)} = {\frac{1}{a_{1}}{\int_{0}^{t}{{C\left( {x,t} \right)}^{a_{2}}{dt}}}}} & (19)\end{matrix}$

The constants a₁ and a₂ are empirical constants and depend on theparticular species and strain of insect. e(x, t) account for the periodof exposure to phosphine that an insect has encountered. For a givenpoint in the grain:

When e(x, t)<1 some measurable number of insects in the grain are stillalive.

When e(x, t)>1 at least 99.9% of the insect population have been killed.

For rhyzopertha dominica a₂=0.6105 and a₁=4.04.

Example 1.5 Phosphine Source

A critical input of the exemplary model is the phosphine release rate ordegassing rate from a phosphine dispenser. Metal phosphides (Mg₃P₂, AlP)are the most common form of phosphine source and are available inpellets, rounds, bags, etc. Degassing rates are a function of time,temperature, pressure and phosphine product and are evaluated by thefollowing model:

Unified degassing model: Degassing rates can be described by a functionof time with a dependence in temperature, pressure and phosphineproduct. A new equation of non-linear regression form may be used todescribe the degassing rate of all phosphine fumigant products:

f(t)=100A ₁(1−exp(−tA ₂))   (20)

A₂ coefficient is a function of phosphine fumigant product and relativehumidity. A new coefficient (A₁) is created to take into account theslower degassing rates for low temperatures:

$\begin{matrix}{A_{1} = {1 - \frac{\left( {20 - T_{air}} \right)^{2}}{300}}} & (21)\end{matrix}$

A₁ and A₂ coefficients depend on commodity

Example 1.6 Calculation of Air Properties

In all calculations it is important to insert accurate values of thethermodynamic and transport properties of air at atmospheric pressure.The correlations proposed by McQuillan et al. (1984) are used:

$\begin{matrix}{\mspace{79mu} {{{Density}:\rho} = {\frac{351.99}{T} + {\frac{344.84}{T^{2}}\mspace{14mu}\left\lbrack \frac{kg}{m^{3}} \right\rbrack}}}} & (22) \\{\mspace{79mu} {{{Viscosity}:\mu} = {\frac{1.4592\mspace{11mu} T^{3/2}}{109.10 + T}\mspace{11mu}\left\lbrack {10^{- 6}\mspace{11mu} \frac{Ns}{m^{2}}} \right\rbrack}}} & (23) \\{\mspace{79mu} {{{Thermal}\mspace{14mu} {{conductivity}:k}} = {\frac{{2.3340 \cdot 10^{- 3}}\mspace{11mu} T^{3/2}}{164.54 + T}\mspace{14mu}\left\lbrack \frac{W}{mK} \right\rbrack}}} & (24) \\{{{Specific}\mspace{14mu} {{heat}:C_{p}}} = {1030.5 - {0.19975\; T} + {{3.9734 \cdot 10^{- 4}}\mspace{11mu} {T^{2}\mspace{11mu}\left\lbrack \frac{J}{{kg}\mspace{11mu} K} \right\rbrack}}}} & (25)\end{matrix}$

Example 1.7 Boundary Conditions

In order to evaluate accurately the storage (computational domain)interaction with its surroundings, the following boundary conditions maybe used:

Example 1.7.1 Mass Convective Boundary Condition

In order to calculate losses of phosphine from the silo walls/holes tothe ambient air, the convective boundary condition may be used:

$\begin{matrix}{\left. {{- D_{m}}\frac{\partial C}{\partial x}} \right|_{x = 0} = {h_{m}\left( {C - C_{amb}} \right)}} & (27)\end{matrix}$

For h_(m)=0 it becomes the zero gradient boundary condition. SinceOpenFoam is not able to handle the above boundary condition, theinstallation of the swak4FOAM library may be necessary and specificallythe use of groovybc boundary condition. h_(m) is a function of silogeometry (cylinder, orthogonal), fluid medium (air, water) and fluidvelocity (e.g. wind velocity). In convective mass transfer, theChurchill-Bernstein equation may be used to estimate the surfaceaveraged Sherwood number for a cylinder in cross flow at variousvelocities:

$\begin{matrix}{{Sh}_{D} = {\frac{h_{m}L}{D_{m}} = {0.3 + {\frac{0.62\; {Re}^{1/2}\mspace{11mu} {Sc}^{1/3}}{\left\lbrack {1 + \left( {0.4/{Sc}} \right)^{2/3}} \right\rbrack^{1/4}}\left\lbrack {1 + \left( \frac{Re}{282000} \right)^{5/8}} \right\rbrack}^{4/5}}}} & (28)\end{matrix}$

Example 1.7.2 Thermal Convective Boundary Conditions

In order to calculate heat transfer on the boundary, the convectiveboundary condition may be used (Barreto et al., 2013)):

$\begin{matrix}{\left. {{- k}\frac{\partial C}{\partial x}} \right|_{x = 0} = {{h_{c}\left( {T - T_{amb}} \right)} - {\alpha_{h}G} + {{\epsilon\sigma}\left( {T^{4} - T_{sky}^{4}} \right)}}} & (29)\end{matrix}$

Where the second term of the right-hand side is the heat gain due tosolar radiation and the third term is the net radiation heat loss ratefor a hot object which is radiating energy to its cooler surrounding(Adelard et al. 1998).

T _(sky)=0.0552T _(amb)√{square root over (T _(amb) )}  (30)

h _(c)=10.45−U _(wind)+10√{square root over (U _(wind))}  (31)

Fumigant Dosage and Treatment Duration Optimization

In certain embodiments, it may be useful to obtain a relatively quickestimate of fumigant dosage for a given crop storage area. For example,a user may provide the dimensions and other characteristics of a cropstorage area and the targeted pest via a user interface such as UI 900,and may initiate a quick estimate of the fumigant dosage by selecting“Calculate & Update” via treatment options 910. Such an estimate may beobtained using a lower-resolution approach compared to the model ofprocess 1200, so that the estimate may be obtained moreefficiently—e.g., by using one-dimensional cells, and not including heattransfer effects, not including velocity or pressure equations, and notincluding wind effects. This novel approach to efficiently estimating aneffective fumigant dosage for a given product, crop storage area, andtargeted pest is described below.

FIG. 13 shows a flow chart for an exemplary process 1300 concerningdetermining a fumigant dosage. First, a server (e.g., server 116) oruser device 112 receives measurement data generated by a plurality ofedge devices 102, where the edge devices may be positioned in variouslocations within a crop storage area 106 (1302). The measurement datamay include, for example, temperature and/or relative humidity. Incertain embodiments, temperature and relative humidity may be obtainedfrom a third-party service, e.g., based on the geographic location ofthe crop storage area 106, or may be provided manually via a userinterface such as UI 900.

Locations within the crop storage area may be represented as a meshdefining a plurality of one-dimensional cells, such that the physicallocations in the crop storage area are mapped to corresponding cells ofthe mesh (1304). For example, the crop storage area may be mapped orprojected onto a mesh of one-dimensional cells having an aggregatelength corresponding to the longest dimension of the crop storage area,and the positions of edge devices may be projected accordingly onto themesh. In certain embodiments, the three-dimensional space of the cropstorage area may be represented in a one-dimensional model bydiscretizing only one of the three dimensions of the crop storage area,such as the length of the crop storage area.

A system of governing differential equations may be defined to relate aplurality of physical descriptors of the contents of the crop storagearea and the environment of the crop storage area, wherein thedescriptors include the amount of fumigant in the crop storage area(1306). For exemplary process 1300, the governing differential equationsshould model fumigant dispersion in a single dimension and may be afunction of the type of product (crop), storage leaks (or gastightness), metal phosphide type and weather conditions.

The initial values of certain physical descriptors may be set using edgedevice 102 measurements of temperature and/or relative humidity thatcorrespond to the temperature and relative humidity measured at thelocation of the respective edge device, and thus characterizing the airand/or crop at the location (1308). Additional initial values ofphysical descriptors may be set based on, for example, known physicalconstants, the type of product, fumigant type and formulation, andweather conditions, the crop storage area volume, the fill percentage ofthe crop storage area, the quantity of product, the expected pest type,whether the pest type is resistant to the fumigant, and the expectedleakage of the crop storage area.

While no effective dosage has been identified, and starting from a lowdosage and increasing by a step with each iteration, the following steps1312 and 1314 will be repeated (1310). For example, in the firstiteration, the initial concentration of fumigant is set in accordancewith a first low dosage of fumigant (i.e., a first candidate dosage). Ina second iteration, the initial concentration of fumigant is setaccording to the sum of the first candidate dosage plus an increment(i.e., a second candidate dosage). As used in process 1300, the termeffective dosage is a dosage of fumigant at the most remote point in thestorage (where the remote point is distant from the fumigantdispenser(s)) resulting a concentration and exposure duration that issufficient to control pests in the crop storage area. In certainembodiments, controlling pests may mean a 99% reduction in pests, 100%reduction in pests, or no measurable amount of pests remaining.

Numerical analysis of the governing differential equations may be usedto simulate the values of the physical descriptors, including the amountof fumigant (starting from a candidate dose), at a range of time pointswithin each cell of the mesh (1312). The simulated physical descriptorsmay include one or more of: sorption, fumigant degassing from a source,leakage, and fumigant diffusion.

A table of minimum exposure times and fumigant concentrations forcontrolling relevant pests may be used to determine whether thecandidate dosage is effective, using the simulated fumigantconcentration (at the most remote point in the storage area across arange of time points) to estimate the resulting fumigant concentrationand duration for the candidate dosage (1314). If the candidate dosage iseffective, the candidate dosage is reported as a recommended dosage fordisplay at a user device, e.g. in response to a request from a userdevice via treatment options 910 (1316).

* * * * *

EXAMPLE 2 A One-Dimensional CFD Model for Estimating an EffectivePhosphine Dosage

In order to calculate the appropriate phosphine dosage for a successfultreatment the model described below may be used. The result (phosphineconcentration on the most remote point of the storage) is a function ofthe commodity, storage leaks (or gas tightness), metal phosphide typeand weather conditions.

Example 2.1 Governing Equations

The equations used by the model and that describe the phosphineconcentration in a storage structure are the following:

$\begin{matrix}{{\varphi \frac{\partial C}{\partial t}} = {{d\frac{\partial^{2}C}{\partial x^{2}}} - {\varphi \; B_{1}C} - {\varphi \; B_{1}C} + {B_{2}q} + {\varphi \; Q_{source}} - {\varphi \; R_{SV}Q_{loss}C}}} & (32) \\{\mspace{79mu} {\frac{\partial q}{\partial t} = {{{- B_{3}}q} + {\varphi \; B_{4}C}}}} & (33)\end{matrix}$

The phenomena taken into account in equations (32) and (33) are:sorption, phosphine degassing from a source, leakage (SVR is the surfaceto volume ratio), and phosphine diffusion.

In order to discretize equations (32) and (33), the Backward Eulermethod is used for the time derivative, which is a fully implicit schemethat provides accurate solutions and stable computations even for largetime steps (compared to explicit schemes):

${\varphi \; \frac{C_{i}^{n + 1} - C_{i}^{n}}{\Delta \; t}} = {\left. {{d\; \frac{C_{i - 1}^{n + !} + {2C_{i}^{n + !}} - C_{i + 1}^{n + !}}{\left( {\Delta \; x} \right)^{2}}} - {\varphi \; B_{1}C_{i}^{n}} - {\varphi \; B_{1}C_{i}^{n}} + {B_{2}q_{i}^{n}} + {\varphi \; Q_{{source},i}^{n}} - {\varphi \; R_{sv}Q_{{loss},i}^{n}C_{i}^{n}}}\rightarrow {C_{i}^{n + 1} - C_{i}^{n}} \right. = {\left. {\frac{\Delta \; {td}}{{\varphi \left( {\Delta \; x} \right)}^{2}}{\left( {C_{i - 1}^{n + 1} - {2C_{i}^{n + 1}} - C_{i + 1}^{n + 1}} \right)++}\frac{\Delta \; t}{\varphi}\left( {{{- \varphi}\; B_{1}C_{i}^{n}} - {\varphi \; B_{1}C_{i}^{n}} + {B_{2}q_{i}^{n}} + {\varphi \; Q_{{source},i}^{n}} - {\varphi \; R_{sv}Q_{{loss},i}^{n}C_{i}^{n}}} \right)}\rightarrow {{{- \frac{\Delta \; {td}}{{\varphi \left( {\Delta \; x} \right)}^{2}}}C_{i - 1}^{n + 1}} + {\left( {1 + {2\; \frac{\Delta \; {td}}{{\varphi \left( {\Delta \; x} \right)}^{2}}}} \right)C_{i}^{n + 1}} - {\frac{\Delta \; {td}}{{\varphi \left( {\Delta \; x} \right)}^{2}}C_{i + 1}^{n + 1}}} \right. = {{C_{i}^{n}++}\frac{\Delta \; t}{\varphi}\left( {{{- \varphi}\; B_{1}C_{i}^{n}} - {\varphi \; B_{1}C_{i}^{n}} + {B_{2}q_{i}^{n}} + {\varphi Q}_{{source},i}^{n} - {\varphi \; R_{sv}Q_{{loss},i}^{n}C_{i}^{n}}} \right)}}}$

The above equation system is tridiagonal which can be solved efficientlyusing the tridiagonal matrix algorithm. The solution can be obtained inO(n) operations instead of O(n³).

Eq. 33 has a simpler discretization form since it has no diffusion term:

$\frac{q_{i}^{n + 1} - q_{i}^{n}}{\Delta \; t} = {\left. {{{- B_{3}}q_{i}^{n}} + {\varphi \; B_{4}C_{i}^{n}}}\rightarrow q_{i}^{n + 1} \right. = {q_{i}^{n} + \left( {{{- B_{3}}q_{i}^{n}} + {\varphi \; B_{4}C_{i}^{n}}} \right)}}$

Neumann boundary conditions may be used, since the value of thederivative is known

$\frac{\partial C}{\partial x} = 0.$

Calculation of the dosage after an iteration: Brent's method may be usedwhich is a root-finding algorithm combining the bisection method, thesecant method and inverse quadratic interpolation. It has thereliability of bisection but it can be as quick as some of theless-reliable methods.

Example 2.2

Leakage rate: In order to take into account leakages that may occurduring a treatment, coefficient Q_(toss)[%/hour] is introduced.Additionally, a surface to volume ratio variable has been defined(R_(sv)) to evaluate storages with larger surfaces and potentiallyhigher leakage rates.

Example 2.3

New moisture availability function: calculates available moisture andissues alerts if it's not sufficient. Moisture content [H₂O gr/m3]available is calculated as a function of temperature and relativehumidity:

MC=(5.018+0.32321T _(air)+0.0081847T _(air) ²+0.00031243T _(air)³)r.h./100   (34)

The demand of moisture according to the phosphine dosage, is equal to:

MC _(d)=1.59·dosage[gr/m3]  (35)

Example 2.4

Unified degassing model: as described in Example 1.

Example 2.5

Sorption: as described in Example 1.

Example 2.6

Fumigation protocols: Calculation of the appropriate phosphine dosagemay be based on several fumigation protocols or according to userspecifications.

For tobacco treatments the CORESTA (2013) protocol may be used:

TABLE 1 Minimum exposure-time required to achieve 100% control of alldevelopment stages of tobacco moth and susceptible cigarette beetle at200 or 300 ppm phosphine at the bale/case centre. Phosphine TobaccoConcentration at the Minimum Exposure Temperature Bale/Case Centre Time[° C.] [° F.] [ppm] [days] 16-20 61-68 300 6 >20 >68 200 4

TABLE 2 Minimum exposure-time required to achieve 100% control of alldevelopment stages of resistant cigarette beetle at 300, 600 or 700 ppmphosphine at the bale/case center. Phosphine Tobacco Concentration atthe Minimum Exposure Temperature Bale/Case Centre Time [° C.] [° F.][ppm] [days] 16-20 61-68 300 12 20-25 68-77 300 12 700 10 >25 >77 300 12600  6

For wheat treatments the GRDC protocol (2011) is considered: 1.5 grPH₃/m³.

Additionally, new fumigation protocols can be developed and used bycompiling the results from bio-assay experiments and correlatingfumigant dosage and duration with insect mortality.

Example 2.7

Oxidative degradation: According to Robinson (1972) residual materialmay be expected to occur following phosphine fumigation of storedproducts. Phosphine oxide is reported as an intermediate in the roomtemperature polymerization of PH₃ and nitric oxide to solid P_(x)H_(y).Robinson reported in his study that phosphorus residues of 2.5 ppm in a1400 ppm atmosphere after 8 days of exposure (approximately 0.17%).Therefore the phenomenon of oxidative degradation is not taken intoaccount in Example 2.

* * * * *

Stored Product Quality: Spoilage Protection

The process of crop storage often involves microbiological contaminationand infestation. The microbial composition is of great importance, sinceat high moisture levels the microorganisms could grow and alter theproperties of product. Product deterioration can also be related torespiration of the product itself and of the accompanyingmicroorganisms.

Safe Product Storage Time

Described below are approaches for determining future moisture contentand temperature in stored product, such as grain, and further using themoisture content and temperature to determine how long the product maycontinue to be safely stored in a particular crop storage area. Previousapproaches for determining a safe storage time (1) assumed a staticmoisture content and temperature for the stored product—i.e., no changein moisture content and temperature over time; (2) applied aspace-averaged assumption, in which the entire crop storage area istreated as having the same conditions/physical descriptors; (3) have notincorporated ambient weather conditions; and (4) have not combinedadvanced mathematical modeling with real-time sensor data. Theapproaches presented here determine, e.g., how moisture content andtemperature have changed and are likely to change over time byincorporating transient conditions from sensor data, determineconditions for each location within a crop storage area in threedimensions, and incorporate ambient weather conditions in determiningthe safe storage time for a product.

FIG. 15 shows a flow chart for an exemplary process 1500 concerningdetermining the safe storage time for a post-harvest crop. First, aserver (e.g., server 116) or user device 112 receives measurement datagenerated by a plurality of edge devices 102, where the edge devices maybe positioned in various locations within a crop storage area 106(1502). The measurement data may include, for example, concentration ofO₂, concentration of CO₂, temperature, moisture, and/or relativehumidity. In certain embodiments, temperature, moisture, and relativehumidity may be obtained from a third-party service, e.g., based on thegeographic location of the crop storage area 106, or may be providedmanually via a user interface such as UI 900.

A portion safe storage time is determined for each portion of aplurality of portions of a stored crop, the respective portionsco-localized with respective edge devices based on the measurement data,and a linear or exponential model for dry matter loss, mold appearance,and/or germination capacity (1504). As used in process 1500, a portionrepresents a portion of the total amount of stored crop that isassociated with a respective edge device, and may be closer to therespective edge device than any other edge device in the crop storagearea 106.

A total safe storage time for the stored crop is determined based on therespective portion safe storage times of step 1504 (1506). For example,the total safe storage time may be the shortest or earliest safe storagetime selected from each portion safe storage time (e.g., the timeassociated with the portion that is predicted to spoil the soonest). Incertain embodiments, the total safe storage time may be a weightedaverage of the portion safe storage times. In certain embodiments, aparticular total safe storage time is determined for different types ofspoilage, such as a visible mold safe storage time, a dry matter losssafe storage time, and a germination safe storage time. The total safestorage time(s) may be reported to a user device and displayed to auser, e.g., via the content panel 1104 of UI 1100.

In certain embodiments, if a portion safe storage time or a total safestorage time falls below a threshold, a component of system 100 maygenerate an instruction to take remedial action. For example, a remedialaction may include generating a notification provided to a user to turnon fans; or automatically generating an instruction for an electricalsystem at the storage area to turn on a particular fan or set of fans.

* * * * *

EXAMPLE 3

Safe Storage Prediction for Corn, Wheat, and Additional Products

The following computational models described below may be used topredict safe storage time (SST), following the approach described inprocess 1500. They have a strong dependency on commodity, temperature(T), grain moisture content (Mw), dry matter loss (DML) and activity ofwater (aw).

Example 3.1 Model 1

Applicable to: Corn

Criterion: dry matter loss

Restrictions:

1<T[° C.]<24; 15<Mw %<30

Equation: SST=v₁+v₂ T+v₃Mw+v₄T²+v₅TMw+v₆Mw²

Coefficients: v₁=3774.98; v₂=−88.12; v₃=−252.55; v₄=0.587; v₅=2.686;v₆=4.223

Source: Kaleta and Gornicki (2013)

Example 3:2 Model 2

Applicable to: Wheat

Criterion: dry matter loss

Restrictions:

4<T[° C.]<40; 15<Mw %<24; 0.25<DML %<1

Equation: SST=exp(v₁+v₂T+v₃Mw+v₄DML)

Coefficients: v₁=6.490336; v₂=−0.024165; v₃=−0.163337; v₄=1.292568

Source: Kaleta and Gornicki (2013)

Example 3.3 Model 3

Applicable to: Wheat, barley, oats, rye

Criterion: appearance of visible molds

Restrictions:

10<T[° C.]<25; 15<Mw %<24

Equation: SST=exp(v₁+v₂T+v₃Mw)

Coefficients:

Wheat:

v₁=50.66928; v₂=−0.272909; v₃=−2.52755

Barley:

v₁=27.04320; v₂=−0.174362; v₃=−1.17856

Oats:

v₁=31.60300; v₂=−0.201594; v₃=−1.55997

Rye:

v₁=34.58371; v₂=−0.283607; v₃=−1.58288

Source: Kaleta and Gornicki (2013)

Example 3:4 Model 4

Applicable to: Wheat, barley, oats, rye

Criterion: germination capacity

Restrictions:

10<T[° C.]<20; 11<Mw %<24

Equation: SST=exp(v₁+v₂T+v₃Mw)

Coefficients:

Wheat:

v₁=12.28039; v₂=−0.128973; v₃=−0.473026

Barley:

v₁=13.12305; v₂=−0.174000; v₃=−0.452103

Oats:

v₁=13.96125; v₂=−0.148378; v₃=−0.604968

Rye:

v₁=10.13185; v₂=−0.087999; v₃=−0.426973

Source: Kaleta and Gornicki (2013)

Example 3.5 Model 5

Applicable to: malting barley

${{Equation}:{SST}} = {{\log \left( \frac{v_{1}}{T} \right)}/{\exp \left( {v_{2} + {v_{3}\mspace{11mu} {aw}}} \right)}}$

Coefficients: v₁=35.0; v₂=−21.22; v₃=20.33

Source: Fleurat-Lessard (2017)

Example 3.6 Model 6

Applicable to: Corn

Restrictions:

2<T[° C.]<32; 12<Mw %<24

Lookup table:

Mw % T ° C. 12 13 14 15 16 18 20 22 24 32 365+ 365+ 251  49 27 10 5 4 329 365+ 365+ 336  66 36 14 7 5 3 27 365+ 365+ 365+ 87 47 18 9 6 4 24365+ 365+ 365+ 117  63 24 12 8 5 21 365+ 365+ 365+ 157  85 32 16 10 7 18365+ 365+ 365+ 210  113  43 22 13 9 16 365+ 365+ 365+ 278  150  57 28 1711 13 365+ 365+ 365+ 365+ 226  86 38 22 14 10 365+ 365+ 365+ 365+ 339 130  50 29 19 7 365+ 365+ 365+ 365+ 365+ 195  66 37 24 4 365+ 365+ 365+365+ 365+ 293  88 48 30 2 365+ 365+ 365+ 365+ 365+ 365+ 115 62 39

Example 3.7 Insect Population Models

Temperature and moisture conditions in grain stores have an impact onthe population growth rate of insect pests. Development rate increasesfrom a lower threshold up to the optimum temperature and then declinesrapidly. In order to evaluate insect population or growth rate, thefollowing equations are used (Driscoll, 2000):

$\begin{matrix}{{N\left( {t + {\Delta \; t}} \right)} = {{N(t)}e^{r_{m}\Delta \; t}}} & (36) \\{\frac{N(t)}{dt} = {N_{o}r_{m}e^{r_{m}\Delta \; t}}} & (37) \\{r_{m} = {{{f^{\prime}\left( {r.h.} \right)}e^{c_{1}T}} + {\ln \left( {c_{2}\left( {T_{m} - T} \right)} \right)}}} & (38) \\{{f^{\prime}\left( {r.h.} \right)} = {c_{3} + {c_{4}\; {r.h.{+ c_{5}}}\; {r.h.^{2}}}}} & (39)\end{matrix}$

Where, T_(m) is the mortality temperature, N_(o) the initial insectpopulation [number of insects/kg of grain]. The model is applicable forthe following species: Rhyzopertha dominica, Sitophilus oryzae,Oryzaephilus surinamensis, Tribolium castaneum

Example 3.8

Determining grain condition for each location, within a crop storagearea, using numerical modeling with sensor data and weather forecastintegration.

In order to analyze grain storage condition and determine the change inconcentration of CO₂ and temperature in silos the mathematical modelproposed by Barreto et al. (2013) is used, but according to certainembodiments of the present invention it is adapted to three dimensionsfrom their two-dimensional model. Such a three-dimensional model has notbeen attempted in previous reports due to computational expense and thedifficulty in adapting such a system to three dimensions. Due to grainand insect respiration, CO₂ and temperature changes are both indicatorsfor grain spoilage. The mathematical model takes into account theweather conditions locally and creates a coupled system in terms oftemperature T, grain moisture content W, oxygen O₂ and carbon dioxideCO₂ concentrations:

$\begin{matrix}{{c_{p}\rho_{bs}\frac{\partial T}{\partial t}} = {{\nabla\left\lbrack {k_{b}\left( {\nabla T} \right)} \right\rbrack} + {\rho_{bs}L_{g}\frac{\partial W_{g}}{\partial t}} + {\rho_{bs}q_{H}Y_{{CO}_{2}}}}} & (40) \\{{\rho_{bs}\frac{\partial W_{g}}{\partial t}} = {{\nabla\left\lbrack {D_{w}\left( {{\eta \cdot {\nabla W_{g}}} + {\omega \cdot {\nabla T}}} \right)} \right\rbrack} + {\rho_{bs}q_{w}Y_{{CO}_{2}}}}} & (41) \\{{\varphi \frac{\partial{CO}_{2}}{\partial t}} = {{\nabla\left\lbrack {D_{{CO}_{2}}\left( {\nabla{CO}_{2}} \right)} \right\rbrack} + {\rho_{bs}r_{{CO}_{2}}}}} & (42) \\{{\varphi \frac{\partial O_{2}}{\partial t}} = {{\nabla\left\lbrack {D_{O_{2}}\left( {\nabla O_{2}} \right)} \right\rbrack} + {\rho_{bs}r_{O_{2}}}}} & (43)\end{matrix}$

Respiration may be modelled by the complete combustion of a typicalcarbohydrate. The rate of CO₂ production r_(CO2) in m³ s⁻¹ kg⁻¹ [drymatter] is given by:

$\begin{matrix}{{r_{{CO}_{2}} = {\frac{Y_{{CO}_{2}}}{1000\mspace{14mu} M_{{CO}_{2}}}\frac{RT}{P_{at}}}}{r_{O_{2}} = r_{{CO}_{2}}}} & (44)\end{matrix}$

The boundary conditions related to the above equations (40)-(44) aregiven by:

$\begin{matrix}{{{- k_{b}}\frac{\partial T}{\partial t}} = {{h_{c}\left( {T - T_{amb}} \right)} - {\alpha \; G} + {{\xi\sigma}\left( {T^{4} - T_{sky}^{4}} \right)}}} & (45) \\{{\sigma \; T_{sky}^{4}} = {\xi_{sky}\sigma \; T_{amb}^{4}}} & (46) \\\begin{matrix}{T = {T_{soil}\left( {y,t} \right)}} \\{= {{T_{1}(y)} + {T_{2}{{\exp\left( {{- y}\sqrt{\frac{2\Psi}{D_{soil}}}} \right)}\left\lbrack {\cos\left( {{\Psi \; t} - {y\sqrt{\frac{2\Psi}{D_{soil}}}} - \phi} \right)} \right\rbrack}}}}\end{matrix} & (47) \\{\frac{\partial p_{u}}{\partial n} = {\left. 0\Rightarrow{\eta \; D_{w}\frac{\partial W_{g}}{\partial n}} \right. = {{- \omega}\; D_{w}\frac{\partial T}{\partial n}}}} & (48) \\{{{- D_{{CO}_{2}}}\frac{\partial{CO}_{2}}{\partial n}} = {\frac{P_{{CO}_{2}}P_{{at}\; m}}{L}\left( {{CO}_{2} - {CO}_{2\; {out}}} \right)}} & (49) \\{{{- D_{O_{2}}}\frac{\partial O_{2}}{\partial n}} = {\frac{P_{O_{2}}P_{{at}\; m}}{L}\left( {O_{2} - O_{2{out}}} \right)}} & (50)\end{matrix}$

The above boundary conditions (45)-(50) take into account solarradiation and convection to the surroundings, as well as the interactionbetween the soil and the bottom layer of the silo. Gas transfer throughthe plastic layer is modelled by defining an equivalent permeability ofthe plastic to O₂ and CO₂. Plastic is assumed impermeable to moisturetransfer.

The value of some parameters which are used as input to the model, oftendeviate from their typical values. For instance, thermal conductivity ofa metal silo may vary due to corrosion or paint. This issue is overcomein embodiments by using real-time sensor data. As the storage periodadvances, model predictions are compared with sensor data at thelocations where sensors are installed (defined in a three-dimensionalspace). An iterative optimization process 2000 is employed, to determineany changes in the input parameter values which improve the agreementbetween the model and sensor data. The outcome of this optimizationprocess is a more accurate model prediction not only applicable to thespecific sensor location(s) but by inference also applicable on theentire storage volume. FIG. 20 shows a flow chart concerning theoptimization process 2000, according to a preferred embodiment.

* * * * *

Heat Treatments

A heat treatment is a popular method for eliminating pests in storagefacilities. During this process, a crop storage area is heated for aspecific time until most or all of pests have been eliminated.

Data Analysis for Heat Treatments

During a heat treatment, the system collects, in frequent intervals,measurements e.g., from edge devices 102 scattered inside the cropstorage area/asset, and stores them in a database (e.g., at local datastore 108 or remote data store 122). The measurements may be sent to ananalytics system (application 120) for processing and prediction offuture temperature values. The analytics system analyzes the datacollected from past treatments and provides an estimation of the futuretemperature values inside the asset for each sensor. The system maypresent the time for successful pest elimination.

FIG. 14 shows a flow chart for an exemplary process 1400 concerningdetermining the duration of a heat treatment. First, a training setincluding a plurality of heat treatment time series is prepared, whereeach respective heat treatment time series is a set of temperaturemeasurements and associated measurement times recorded from a singleedge device 102 or temperature sensor (1402). The plurality of heattreatment time series should represent many different heat treatments,and it is desirable to include many different time series for each ofthe heat treatments. For example, the time series may representmeasurements taken by edge devices distributed at positions throughoutmany different crop storage areas, for different types of crops, andduring different seasons and at different geographic locations, in orderto capture the full range of diversity of heat treatment time series andrepresent that diversity in the training set.

The training set of time series may be clustered using a k-shape-baseddistance method (1404). See, e.g., FIG. 16 showing 40 example resultingclusters of temperature traces from heat treatments.

A time series centroid may be extracted from each cluster to representthe respective cluster (1406) That is, the extracted centroid is a timeseries having the form of a series of temperatures associated withtimes. The centroids may be stored (e.g., in local data store 108 orremote data store 122) as exemplars of the expected course of a heattreatment.

An in-progress heat treatment applied to a current crop storage area maybe evaluated based on the trained system. A server (e.g., server 116) oruser device 112 receives measurement data generated by a plurality ofedge devices 102, where the edge devices may be positioned in variouslocations within a current crop storage area 106 (1408). The measurementdata includes temperature measurements and the times for themeasurements. In certain embodiments, the received measurement data mayinclude thermal camera images.

The received temperature data is arranged into a respective current timeseries for each respective edge device in the current crop storage area(1410). The most similar time series centroid in the training set may beidentified for each current time series, e.g., by calculating the sum ofsquared distances between each current time series and a database ofexemplar centroids (1412). The expected course of future temperaturesfor each current time series may be estimated in accordance with themost similar centroid (1414). Based on the heat tolerance (temperature,duration) for the targeted pest, the predicted course of treatment maybe estimated as having with the shape of the most similar centroids(1416). For example, if four edge devices are used in a current heattreatment, four centroids will be identified to represent the expectedcourse of treatment for the four positions in the crop storage areawhere the four edge devices are located. In certain embodiments, therange of the duration of treatment may be reported using the centroidsassociated with the best and worst edge node positions and correspondingmeasurements. For example, the shape of the centroid, as aligned to thecurrent temperature series, may be used to generate a projection of theexpected temperature at various future time points, and the durations ofthe expected temperatures may be used to determine the amount of timeuntil the targeted pest cannot survive. See, e.g., FIG. 17, showingexemplary temperature traces from heat treatments and predictedtemperatures, described below in connection with Example 4.

* * * * *

EXAMPLE 4 Heat Treatments Example 4.1 Predictive Analytics Example 4.1.1Training

One of the primary tasks of the predictive analytics approach is toperform accurate predictive analytics of sensor data to estimate futurevalues and to achieve that a number of tasks need to be completed.Firstly, we gather historical data to serve as a training set. Weperform dataset reduction by choosing a sampling rate of, preferably, 15minutes since the collected data has varying time intervals and thesensors' data length may differ. By implementing data manipulationfunctions, time series are “forced” to have similar time and lengthreadings for all sensors. Information is not lost from problematicsensors, for instance with a small amount of readings (malfunctioning)have already been removed. Some time series have missing values whichare interpolated filling with additional data and consequently theseries resulting are of the same length and calculated metrics are ofspecific timestamps (15 minutes, 1 hour, etc.). In the second step, astime series data exhibit noise the need for removing it and producingsmoother data is important. The method used is low-pass filtering andpreferably the type of signal processing filter is the Butterworthfilter. After applying filtering to raw data, a new smoothest version ofsensor readings is obtained.

As the number of edge devices may be large, the time-series data areoften high dimensional and slow down the analysis process. Clusteringentails grouping temperature time series that are similar to each otherand extracts information from unlabeled data.

Multiple distance measures can be used to find clusters among timeseries by calculating the distance among them. A shape-based distancemethod, where sequences exhibit similar patterns (the distance is thesmallest), are grouped into the same cluster based on their shapesimilarity regardless of differences in amplitude and phase. Thisdistance is based on coefficient normalization and cross-correlationdistance (J. Paparrizos, L. Gravano, 2016) between pairs of sensorsamong time series without having necessarily the same length. So, as afirst step the cross-distance matrix is calculated and z-normalized asthe distance works better that way for the sensors readings inside thetraining set. In the next step, time series clustering is performedchoosing k clusters and calculating the centroids using partitionmethods where each cluster has a centroid that is also time series. (SeeFIG. 16.) This results in multiple clusters and their centroids thatstored for further usage. To conclude the training process, a smallamount of historical data serves as a testing set where the performanceof the clustering, the centroids and the prediction process is tested,resulted in an error that needs to be as small as possible, meaning thatthe predicted values and the actual are close.

Example 4.1.2 Prediction

When a new treatment takes place, new time series arrive from heattreatments, the new data are preprocessed as mentioned and grouped toalready existed clusters based on the k-shaped distance method thatminimizes the sum of squared distances between new series and theclusters' centroids. When the new time series have been successfullygrouped into new clusters the clusters' centroids are used to predictnew values.

FIG. 17 shows exemplary temperature traces from heat treatments.Prediction time indicator 1702 separates actual measurements frompredicted temperatures based on the shape of the most similarcentroids—i.e., marker 1702 indicates the current time in minutes frombeginning of the treatment when the future temperature courses weredetermined.

Example 4.2 Impact of Heat on Pests

Pests can survive the exposure of high temperatures for a limited amountof time. As heat tolerance differs between pests, the system may beconfigured to determine the best elimination protocol for each pest.Based on each protocol, the temperature should stay above a certainthreshold for specific time to achieve a successful elimination ofpests. The heat tolerance of pests for each elimination protocol isdescribed in the following tables:

Heat tolerance of tribolium confusum - Kansas state university 2008Temperature threshold(Celsius) 46 48 50 52 54 56 Time for 99% 700 198 9047 32 19.9 elimination(mins)

Heat tolerance of tribolium castaneum - Kansas state university 2003Temperature 50 54 58 60 threshold(Celsius) Time for 99% 572 208 76 66elimination(mins)

Heat tolerance of hemidactylus turcicus - CSL 2005 Temperature 47 49 5153 threshold(Celsius) Time for 99% 420 120 30 18 elimination(mins)

Heat tolerance of bed bugs - University of Florida 2009 Temperature 4143 45 47 49 threshold(Celsius) Time for 99% 100 25 4 2.5 1elimination(mins)

Nomenclature and Abbreviations

AR aspect ratio AR=H/L

C phosphine concentration

C_(ref) reference concentration

C_(p) specific heat under constant pressure [J kg⁻¹ K⁻¹]

D_(a) Darcy number [m² s⁻¹] D_(a)=K/L²

D_(m) binary diffusion coefficient [m² s⁻¹]

D_(w) effective diffusivity parameter for water vapour

dp solid particle diameter [m]

F is the partition relation coefficient

g magnitude of the gravitational acceleration, g=9.81 [m s⁻²]

G solar radiation [W m⁻²]

Gr thermal Grashof number Gr=g β H³ _(in)ΔT/ν²

Gr_(c) solutal Grashof number Gr=g β H³ _(in)ΔC/ν²

h_(c) heat transfer coefficient

h_(m) mass transfer coefficient

H characteristic height [m]

k thermal conductivity [W m⁻¹ K⁻¹]

K permeability of the porous matrix [m²], the ability to allow the fluidto flow through

k_(f) linear mass transfer coefficient used in sorption modelling

k binding coefficient for irreversible reaction/binding of the adsorbedfumigant in the grain kernel

L characteristic length [m]

Le Lewis number Le=Sc/Pr

L_(g) latent heat of vaporisation of moisture in grain

MW molecular weight [kg mol⁻¹]

N Buoyancy ratio N=Gr_(c)/Gr

p pressure [N m⁻²]

Pr Prandtl number Pr=ν/α

R_(fill) is the filling ratio of stored product to asset volume

Ra Rayleigh number Ra=gβ(T_(h)−T_(c))H³/(να)

Re Reynolds number based on the height of the tank Re=u_(ref)L/v

Sc Schmidt number Sc=ν/Dm

S_(sorp) specific adsorption surface area

t physical time [s]

T local temperature [K]

T_(ref) reference temperature [K]

u, v Cartesian velocity components [m s⁻¹]

U_(wind) wind velocity [m s⁻¹]

x, y coordinate distance along the length and height of the tank [m]

Greek Symbols

α thermal diffusivity [m² s⁻¹]

α_(h) absorptivity

β volumetric expansion coefficient for temperature

$\beta = {{- \frac{1}{\rho}}{\left( \frac{\partial\rho}{\partial T} \right)_{p}\mspace{11mu}\left\lbrack K^{- 1} \right\rbrack}}$

β_(c) species expansion coefficient, [m³ kg⁻¹]

ε emissivity

η change in partial pressure due to change in the moisture content atconstant temperature

μ dynamic viscosity

ν kinematic viscosity [m² s⁻¹]

ρ density [kg m⁻³]

ρ_(bs) dry bulk density [kg m⁻³]

φ porosity

$\phi = \frac{{pore}\mspace{14mu} {volume}}{{total}\mspace{14mu} {volume}}$

σ Stefan Boltzmann coefficient

τ tortuosity,

$\tau = \frac{{curve}\mspace{14mu} {length}}{{distance}\mspace{14mu} {between}\mspace{14mu} {ends}}$

ω change in partial pressure due to change in temperature at constantmoisture content

REFERENCES

L. Adelard, F. Pignolet-Tardan, T. Mara, P. Lauret, F. Garde, H. Boyer,Sky temperature modelisation and applications in building simulation,Renewable Energy, Volume 15, Issue 1, 1998, Pages 418-430.

A. Barreto, A. Rita, G. Analia, B. Ricardo, Analysis of storageconditions of a wheat silo-bag for different weather conditions bycomputer simulation. Biosystems Engineering 116, pp. 497-508 (2013).

P. J. Collins, G. J. Daglish, H. Pavic, and R. A. Kopittke. Response ofmixed-age cultures of phosphine-resistant and susceptible strains oflesser grain borer, rhyzopertha dominica, to phosphine at a range ofconcentrations and exposure periods. Journal of Stored ProductsResearch, 41:373-385, 2005.

CORESTA, Phosphine fumigation parameters for the control of cigarettebeetle and tobacco moth. CORESTA guide No 2 (October 2013).

J. A Darby. A kinetic model of fumigant sorption by grain using batchexperimental data. Pest Management Science, 64(5):519-526, 2008.

R Driscoll, B. C Longstaff, S Beckett, Prediction of insect populationsin grain storage, Journal of Stored Products Research, Volume 36, Issue2 (2000).

F. Fleurat-Lessard, Integrated management of the risks of stored grainspoilage by seedborne fungi and contamination by storage mouldmycotoxins—An update, Journal of Stored Products Research, Volume 71(2017).

W. He, W. Lv, and J. Dickerson. Gas transport in oxide fuel cells.Springer International Publishing, New York, USA (2014).

G R D C, Fumigating with phosphine, other fumigants and controlledatmospheres, A grains industry guide. Grains Research and DevelopmentCorporation (2011).

Z. M. Isa, T. W. Farrell, G. R. Fulford, and N. A. Kelson. Mathematicalmodelling and numerical simulation of phosphine flow during grainfumigation in leaky cylindrical silos. Journal of Stored ProductsResearch, 67:28-40, 2016.

A. Kaleta, and K. Gornicki. Criteria of Determination of Safe GrainStorage Time—A Review, Advances in Agrophysical Research, chapter 12(2013)

McQuillan, F. J., Culham, J. R., and Yovanovich, M. M., Properties ofDry Air as One Atmosphere, Microelectronics Heat Transfer Lab., Rept.UW/M HTL 8406 G-01, Univ. of Waterloo, Waterloo, ON, Canada, 1984.

S. Neethirajan, D. S. Jayas, N. D. G. White, and H. Zhang. Investigationof 3d geometry of bulk wheat and pea pores using x-ray computedtomography images. Computers and Electronics in Agriculture,63(2):104-111, 2008.

J. R. Robinson. Residues containing phosphorus following phosphinetreatment: Measurement by neutron activation. Journal of Stored ProductsResearch, 8(1):19-26, 1972.

L. Shen and Z. Chen. Critical review of the impact of tortuosity ondiffusion. Chemical Engineering Science, 62(14):3748-3755, 2007.

John Paparrizos, Luis Gravano, k-Shape: Efficient and AccurateClustering of Time Series, ACM SIGMOD Record, v.45 n.1, 2016.

FIG. 19 depicts a block diagram of an exemplary computing system 1900that is representative any of the computer systems or electronic devicesdiscussed herein. Note that not all of the various computer systems haveall of the features of system 1900. For example, systems may not includea display inasmuch as the display function may be provided by a clientcomputer communicatively coupled to the computer system or a displayfunction may be unnecessary.

System 1900 includes a bus 2506 or other communication mechanism forcommunicating information, and processor(s) 2504 coupled with the bus2506 for processing information. Computer system 1900 also includes amain memory 2502, such as a random-access memory or other dynamicstorage device, coupled to the bus 2506 for storing information andinstructions to be executed by processor 2504. Main memory 2502 also maybe used for storing temporary variables or other intermediateinformation during execution of instructions to be executed by processor2504.

System 1900 includes a read-only memory 2508 or other static storagedevice coupled to the bus 2506 for storing static information andinstructions for the processor 2504. A storage device 2510, which may beone or more of a hard disk, flash memory-based storage medium, magnetictape or other magnetic storage medium, a compact disc (CD)-ROM, adigital versatile disk (DVD)-ROM, or other optical storage medium, orany other storage medium from which processor 2504 can read, is providedand coupled to the bus 2506 for storing information and instructions(e.g., operating systems, applications programs and the like).

Computer system 1900 may be coupled via the bus 2506 to a display 2512for displaying information to a computer user. An input device such askeyboard 2514, mouse 2516, or other input devices 2518 may be coupled tothe bus 2506 for communicating information and command selections to theprocessor 2504. Communications/network components 2520 may include anetwork adapter (e.g., Ethernet card), cellular radio, Bluetooth radio,NFC radio, GPS receiver, and antennas used by each for communicatingdata over various networks, such as a telecommunications network or LAN.

The processes referred to herein may be implemented by processor 2504executing appropriate sequences of computer-readable instructionscontained in main memory 2502. Such instructions may be read into mainmemory 2502 from another computer-readable medium, such as storagedevice 2510, and execution of the sequences of instructions contained inthe main memory 2502 causes the processor 2504 to perform the associatedactions. In alternative embodiments, hard-wired circuitry orfirmware-controlled processing units (e.g., field programmable gatearrays) may be used in place of or in combination with processor 2504and its associated computer software instructions to implement theinvention. The computer-readable instructions may be rendered in anycomputer language including, without limitation, Python, Objective C,C#, C/C++, Java, Javascript, assembly language, markup languages (e.g.,HTML, XML), and the like. In general, all of the aforementioned termsare meant to encompass any series of logical steps performed in asequence to accomplish a given purpose, which is the hallmark of anycomputer-executable application. Unless specifically stated otherwise,it should be appreciated that throughout the description of the presentinvention, use of terms such as “processing”, “computing”,“calculating”, “determining”, “displaying”, “receiving”, “transmitting”or the like, refer to the action and processes of an appropriatelyprogrammed computer system, such as computer system 1900 or a similarelectronic computing device, that manipulates and transforms datarepresented as physical (electronic) quantities within its registers andmemories into other data similarly represented as physical quantitieswithin its memories or registers or other such information storage,transmission or display devices.

Embodiments

Embodiment A. A system for post-harvest crop quality and pest managementemploying sensor devices that transmit signals wirelessly from insideproduct storage areas.

The system of Embodiment A whereby sensor devices are fumigant sensingdevices that form mesh data networks.

The system of Embodiment A whereby sensor devices are temperature orhumidity sensing devices that form mesh data networks.

The system of Embodiment A whereby sensor devices are housed in plasticenclosures sealed using one or more O-rings to protect the electronicsfrom corrosion by chemicals such as phosphine and employ a magnetic orsimilar contactless method for activation and deactivation.

The system of Embodiment A whereby sensor devices can be calibrated bythe end user using a cloud-connected appliance that records calibrationcoefficients in the cloud and uses coefficients from multiple devices toimprove overall sensor accuracy and device useful life.

The system of Embodiment A whereby sensor devices employ an antennadesigned as a short inverted-L monopole with an orthogonal meander linetop plate having a total line length of approximately a quarterwavelength, to provide for improved transmission characteristics frominside crop storage areas.

Embodiment B. A method for post-harvest crop quality and pest managementemploying sensor devices that transmit signals wirelessly from insideproduct storage areas.

The method of Embodiment B that fuses data from said sensor devices withdata from weather stations to improve predictions.

The method of Embodiment B that employs clustering data analyticsmethods to provide predictions of pest treatment duration, success andother key metrics.

The method of Embodiment B that employs CFD simulations to providepredictions and prescriptions of pest treatments such as phosphinefumigations.

The method of Embodiment B that employs CFD simulations andcomputational models to provide predictions of stored product qualitysuch as safe storage time, insect infestation risk, dry matter loss andgermination capacity.

The method of Embodiment B that employs CFD simulations and data fromsensors to provide predictions of physical quantities in-between sensorlocations.

The method of Embodiment B that employs CFD simulations and data fromsensors to predict the worst-case fumigant levels inside stored productsin a fumigation treatment.

The method of Embodiment B implemented as a cloud-hosted application andaccessible from mobile, wearable and desktop devices.

Embodiment 1. An edge device, comprising:

a plastic housing comprising:

a cap having a first threaded portion and a plurality of ventsconfigured to allow air passage from the environment of the edge deviceinto an environment-exposed compartment;

an upper housing having a second threaded portion, a third threadedportion, and an upper surface containing a sensor opening; and

a lower housing having a fourth threaded portion, wherein the firstthreaded portion of the cap is configured to mate with the secondthreaded portion of the upper housing, and the third threaded portion ofthe upper housing is configured to mate with the fourth threaded portionof the lower housing, such that when assembled the cap and the upperhousing define the environment-exposed compartment, and the upperhousing and the lower housing define a sealed compartment;

an electrochemical gas sensor comprising a sensor cell and a sensorcircuit board, wherein the electrochemical gas sensor is partiallydisposed within the sealed compartment and is fixed in a positionabutting the upper surface of the upper housing such that the sensorcell protrudes into the sensor opening to form a surface of theenvironment-exposed compartment;

one or more upper rubber o-rings circumferentially disposed around aportion of the electrochemical gas sensor that protrudes into theenvironment-exposed compartment to create a seal that abuts the sensoropening of the upper housing;

a main circuit board disposed within the sealed compartment andcommunicatively coupled to the electrochemical gas sensor, the maincircuit board having a plurality of mounted components respectivelycoupled to a battery, a reed switch, an antenna, and radio frequency(RF) circuitry;

a magnet disposed on a first plastic ring, and a second plastic ring,wherein the first plastic ring is configured to rotate around the fourththreaded portion of the lower housing, disposed between the upperhousing and the second plastic ring, such that the magnet is arranged tointeract with the reed switch by the rotation of the first plastic ring,and the second plastic ring is configured to mate with the fourththreaded portion of the lower housing; and

one or more lower rubber o-rings disposed at the interface between theupper housing and the lower housing.

Embodiment 2. The edge device of embodiment 1, wherein the housing isformed from an acetal plastic, such as an acetal copolymer.

Embodiment 3. The edge device of embodiment 1, wherein the vents aremicro holes.

Embodiment 4. The edge device of embodiment 1, wherein the battery is alithium thionyl chloride battery.

Embodiment 5. The edge device of embodiment 1, wherein the monopoleantenna is a short inverted-L monopole antenna with an orthogonalmeander line top plate having a total line length of a nominal quarterwavelength.

Embodiment 6. The edge device of embodiment 1, wherein the first plasticring is rotatable between two detents representing “on” and “off”positions.

Embodiment 7. The edge device of embodiment 1, wherein the number ofupper rubber o-rings is two.

Embodiment 9. A system comprising:

a plurality of edge devices and a gateway device, the plurality of edgedevices and the gateway device collectively forming a mesh network, thegateway device communicatively connected to the internet, the pluralityof edge devices arranged within a storage area and the gateway devicepositioned outside of the storage area, each edge device of theplurality comprising:

a housing having a cylindrical or bell-shaped form, the housingcomprising a battery pack compartment and a second compartment, whereinthe battery pack compartment is separated from the second compartment bya physical safety layer;

one or more sensor devices disposed within the second compartment of thehousing, each sensor device configured to obtain a measurement of thelocal physical environment, and wherein a sensor cell of the one or moresensor devices is positioned adjacent to one or more vents in thehousing such that the sensor cell is in fluid contact with the localphysical environment;

a network component disposed within the housing and communicativelycoupled to the one or more sensor devices, the network componentconfigured to communicate as a node in the mesh network, wherein thenetwork component comprises an antenna; and

a battery pack disposed within the battery pack compartment of thehousing.

Embodiment 10. The system of embodiment 9, wherein a first one of theone or more sensor devices comprises the sensor cell, the sensor cellconfigured for sensing a gas, the gas selected from the group consistingof phosphine, carbon dioxide, and oxygen.

Embodiment 11. The system of embodiment 9, wherein the one or moresensor devices comprise a sensor device selected from the groupconsisting of a thermal camera, a moisture sensor, a humidity sensor,and a temperature sensor.

Embodiment 12. The system of embodiment 9, wherein the antenna is ashort inverted-L monopole antenna with an orthogonal meander line topplate having a total line length of a nominal quarter wavelength.

Embodiment 13. The system of embodiment 9, wherein the housing furthercomprises two or more o-rings to seal sensor-component-associatedopenings of the housing.

Embodiment 14. The system of embodiment 9, wherein the housing furthercomprises a magnetic switch configured to control activation of the oneor more sensor devices.

Embodiment 15. A method for managing post-harvest fumigation treatmentto exterminate pests, comprising:

i. at a server, receiving measurement data generated by a plurality ofedge devices placed inside a storage area, wherein the measurement dataconcerns measurements of a respective local physical environment for arespective edge device at a respective location within the storage area;

ii. representing locations within the storage area as a mesh defining aplurality of three-dimensional cells, wherein locations within thestorage area are mapped to corresponding cells;

iii. defining a system of governing differential equations that relate aplurality of physical descriptors of the contents of the storage areaand the environment of the storage area, wherein the plurality ofphysical descriptors includes the amount of fumigant in the storagearea;

iv. simulating the amount of fumigant within each cell of the mesh bysteps comprising:

setting initial values of a subset of the plurality of physicaldescriptors using a portion of the received measurement data, whereinthe portion of the received measurement data comprises temperature andrelative humidity; and

using numerical analysis of the system of governing differentialequations to approximate the values of the physical descriptors at arange of time points, including the amount of fumigant;

v. optionally, assessing treatment completion by:

determining the amount of living pests for the range of time points,based on the simulated amounts of fumigant in the mesh across the rangeof time points;

identifying the time points associated with an amount of living peststhat is equal to or less than an acceptable amount based on the inferredamount of living pests and inferring a corresponding time remaining fora complete fumigation treatment; and

providing a continuously updated estimate for the time remaining for acomplete fumigation treatment.

Embodiment 16. The method of embodiment 15, wherein the system ofgoverning differential equations includes a representation of heattransfer effects, and a mass boundary condition that depends on wind.

Embodiment 17. The method of embodiment 15, wherein the method furthercomprises:

identifying discrepancies between the simulated and actual amounts offumigant, wherein the portion of the received measurement data furthercomprises fumigant amounts and the associated locations for themeasurements;

based on the identified discrepancies, identifying a location forincreasing fumigant within the storage area that is optimal for reducingthe time remaining for a complete fumigation treatment based on thesimulated concentrations of fumigant; and

providing an instruction to add or move a fumigant dispenser to theoptimal location.

Embodiment 18. The method of embodiment 15, wherein the method furthercomprises:

determining the difference between the simulated and actual amounts offumigant, wherein the portion of the received measurement data furthercomprises fumigant amounts and the associated locations for themeasurements, wherein the difference is calculated as an average acrossthe measurements from different locations within the storage area;

if the difference indicates that the actual amounts are significantlylower than the predicted amounts, providing an instruction to place aspecified additional fumigant dose into the storage area; otherwise, notproviding the instruction.

Embodiment 19. The method of embodiment 15, wherein the storage area isa silo, shipping container, or vessel hold.

Embodiment 20. The method of embodiment 15, wherein receivingmeasurement data generated by a plurality of edge devices comprisesreceiving real-time updates of measurement data.

Embodiment 21. The method of embodiment 15, wherein the physicaldescriptors further comprise temperature and relative humidity.

Embodiment 22. A method for determining post-harvest crop fumigationdosage, comprising:

at a server, receiving measurement data generated by a plurality of edgedevices placed inside a storage area, wherein the measurement dataconcerns measurements of a respective local physical environment for arespective edge device at a respective location within the storage area;

representing locations within the storage area as a mesh defining aplurality of one-dimensional cells, wherein locations within the storagearea are mapped to corresponding cells;

defining a system of governing differential equations that relate aplurality of physical descriptors of the contents of the storage areaand its environment, wherein the plurality of physical descriptorsincludes the amount of fumigant in the storage area;

simulating the amount of fumigant within each cell of the mesh by stepscomprising:

setting initial values of a subset of the plurality of physicaldescriptors using a portion of the received measurement, wherein theportion of the received measurement data comprises temperature andrelative humidity; and

for each candidate dosage in a series of fumigant dosages used as theinitial value for the fumigant, increasing from a small dosage to alarge dosage, while no effective dosage has been identified:

using numerical analysis of the system of governing differentialequations to simulate the values of the physical descriptors, includingthe amount of fumigant, at a range of time points within each cell ofthe mesh;

determining whether the candidate dosage is effective based on a tableof minimum exposure times required to control relevant pests, and thesimulated amount of fumigant within each cell of the mesh after anelapsed period of simulation time; and

providing the candidate dosage as an effective dosage if it isdetermined to be effective, otherwise continuing with an increasedfumigant dosage.

Embodiment 23. The method of embodiment 22, wherein the storage area isa silo, shipping container, or vessel hold.

Embodiment 24. The method of embodiment 22, wherein receivingmeasurement data generated by a plurality of edge devices comprisesreceiving real-time updates of measurement data.

It is to be understood that the above description is intended to beillustrative, and not restrictive. Many other embodiments will beapparent to those of skill in the art upon reviewing the abovedescription. The scope of the invention should, therefore, be determinedwith reference to the appended claims, along with the full scope ofequivalents to which such claims are entitled.

What is claimed is:
 1. A method for managing a current post-harvest cropheat treatment in a current storage area, comprising: at a server,preparing a training set of heat treatment time series comprisingtemperature measurements generated by a first plurality of edge devicesplaced inside a variety of training storage areas, wherein thetemperature measurements comprise measurements of a respective localtemperature for a respective edge device at a respective location withinthe respective training storage area across a respective range of timepoints; clustering each time series of the training set of heattreatment time series using a k-shape-based distance method to generatea plurality of time series clusters, each time series cluster having atime axis; extracting a respective plurality of cluster centroids for arange of points along the time axis of the respective cluster from theplurality of time series clusters; at the server, receiving currenttemperature measurement data generated by a current plurality of edgedevices placed inside the current storage area, wherein the currenttemperature measurement data comprises one or more measurements of arespective local temperature for a respective edge device at arespective location within the current storage area; arranging thetemperature measurements into a respective current time series for eachrespective edge device in the current storage area; calculating the sumof squared distances between each current time series and the centroidsassociated with each time series cluster; assigning each current timeseries to the respective time series cluster associated with thesmallest sum of squared distances; based on the centroids for eachassigned cluster, identifying the expected temperatures at therespective locations within the current storage area for a range offuture time points; based on the current time series, expectedtemperatures at the respective locations, and a protocol for pest heattolerance, providing an estimate of the duration for the currentpost-harvest crop heat treatment.
 2. The method of claim 1, whereinpreparing the training set comprises interpolating missing data andprocessing the training set with a low-pass filter.
 3. The method ofclaim 1, wherein the centroid is a time series.
 4. A method for managingpost-harvest stored crop quality and marketability, comprising: at aserver, receiving measurement data generated by a plurality of edgedevices placed inside a storage area, wherein the measurement dataconcerns measurements of a respective local physical environment for arespective edge device at a respective location within the storage area,and wherein the measurements are either or both temperature and relativehumidity; determining a portion safe storage time for each portion of aplurality of portions of a stored crop, the respective portionsco-localized with respective edge devices of the plurality of edgedevices based on the measurement data and a linear model or exponentialmodel for dry matter loss, mold appearance, or germination capacity;determining a total safe storage time for the stored crop based on therespective portion safe storage times for the plurality of portions ofthe stored crop; and providing the total safe storage time.
 5. Themethod of claim 4, wherein determining the portion safe storage time foreach portion of the plurality of portions is further based on athree-dimensional mathematical model and the measurement data, whereinthe measurement data includes both temperature and relative humidity. 6.The method of claim 4, wherein determining the portion safe storage timeis additionally based on external weather conditions at a geographicsite for the storage area as coupled to the temperature, moisture,oxygen, and carbon dioxide concentrations inside the storage area. 7.The method of claim 4, wherein determining the portion safe storage timeis additionally based on an insect population reported by a plurality ofedge devices.
 8. The method of claim 4, wherein the total safe storagetime is determined as the earliest portion safe storage time or aweighted average of the portion safe storage times.